Physics · JEE Main, NEET

Oscillations

194 practice questions with a worked solution for each. Tap an option to see instantly if you are right.

152MCQ42Numerical26With diagram
Start with question 1 See it move: Simple pendulum
  1. 1A particle executes SHM of amplitude AA. At what displacement xx from mean position is kinetic energy equal to potential energy?JEE Main/MCQ/Medium
  2. 2The time period of a simple pendulum of length LL on the surface of the Moon (gm=g/6g_m = g/6) will:NEET/MCQ/Medium
  3. 3A horizontal spring-mass system with m=2 kgm=2\,\text{kg} and k=200 N/mk=200\,\text{N/m} oscillates with amplitude 0.1 m0.1\,\text{m}. Maximum speed of mass is:JEE Main/MCQ/Medium
  4. 4A particle is executing simple harmonic motion. Its amplitude is AA and time period is 55 sec. The time required by it to move from x=Ax = A to x=A2x = \dfrac{A}{\sqrt{2}} is _______ sec.JEE Main/MCQ/Medium/Simple Harmonic Motion
  5. 5Match List-I with List-II.
    List-IList-IIA.     sin⁡2ωt\sin^2 \omega tI. Periodic with time period T=πωT = \dfrac{\pi}{\omega} but not simple harmonic motion (SHM)B. sin⁡3(2ωt)\sin^3(2\omega t)II. Periodic with time period T=2πωT = \dfrac{2\pi}{\omega} but Not SHMC. sin⁡(ωt)+cos⁡(πωt)\sin(\omega t) + \cos(\pi \omega t)III. Periodic with time period T=πωT = \dfrac{\pi}{\omega} and SHMD. cos⁡ωt+cos⁡2ωt\cos\omega t + \cos 2\omega tIV. Non-periodic
    Choose the correct answer from the options given below :    JEE Main/MCQ/Medium/Simple Harmonic Motion
  6. 6The velocity of a particle executing simple harmonic motion along xx-axis is described as v2=50−x2v^2 = 50 - x^2, where xx represents displacement. If the time period of motion is x7\dfrac{x}{7} s, the value of xx is _____.JEE Main/Numerical/Medium/Simple Harmonic Motion
  7. 7The equation of motion of a particle is given by x=asin⁡(50t+π3)x = a \sin\left(50t + \dfrac{\pi}{3}\right) cm. The particle will come to rest at time t1t_1 and it will have zero acceleration at time t2t_2. The t1t_1 and t2t_2 respectively are _______.JEE Main/MCQ/Medium/Simple Harmonic Motion
  8. 8As shown in the figure, a spring is kept in a stretched position with some extension by holding the masses 1 kg and 0.2 kg with a separation more than spring natural length and are released. Assuming the horizontal surface to be frictionless, the angular frequency (in SI unit) of the system is : k=150 N/mk=150 \mathrm{~N} / \mathrm{m}
    JEE Main/MCQ/Medium/Simple Harmonic Motion/With diagram
  9. 9A cylindrical block of mass MM and area of cross section AA is floating in a liquid of density ρ\rho and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is ____\_\_\_\_.JEE Main/MCQ/Medium/Simple Harmonic Motion
  10. 10A particle is subjected two simple harmonic motions as :
    x1=7sin⁡5tcm\mathrm{x}_1=\sqrt{7} \sin 5 \mathrm{tcm}
    and     x2=27sin⁡(5t+π3)cmx_2=2 \sqrt{7} \sin \left(5 t+\frac{\pi}{3}\right) \mathrm{cm}
    where x is displacement and     tt is time in seconds. The maximum acceleration of the particle is x×10−2 ms−2\mathrm{x} \times 10^{-2} \mathrm{~ms}^{-2}. The value of x is :    JEE Main/MCQ/Medium/Simple Harmonic Motion
  11. 11Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1k_1 and k2k_2, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of AA to the maximum velocity of BB isJEE Main/MCQ/Medium/Simple Harmonic Motion
  12. 12A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm . If D and d are the total distance and displacement covered by the particle in 12.5 s , then Dd\frac{\mathrm{D}}{\mathrm{d}} isJEE Main/MCQ/Medium/Simple Harmonic Motion
  13. 13The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes of 4 m,2 ms−14 \mathrm{~m}, 2 \mathrm{~ms}^{-1} and 16 ms−216 \mathrm{~ms}^{-2} at a certain instant. The amplitude of the motion is x, m\sqrt{x}, \mathrm{~m} where xx is ________JEE Main/Numerical/Medium/Simple Harmonic Motion
  14. 14An object of mass 0.2 kg0.2 \mathrm{~kg} executes simple harmonic motion along x\mathrm{x} axis with frequency of (25π)Hz\left(\frac{25}{\pi}\right) \mathrm{Hz}. At the position x=0.04 mx=0.04 \mathrm{~m} the object has kinetic energy 0.5 J0.5 \mathrm{~J} and potential energy 0.4 J0.4 \mathrm{~J}. The amplitude of oscillation is _____cm\mathrm{cm}.JEE Main/Numerical/Medium/Simple Harmonic Motion
  15. 15A particle is doing simple harmonic motion of amplitude 0.06 m0.06 \mathrm{~m} and time period 3.14 s3.14 \mathrm{~s}. The maximum velocity of the particle is _______ cm/s\mathrm{cm} / \mathrm{s}.JEE Main/Numerical/Medium/Simple Harmonic Motion
  16. 16The displacement of a particle executing SHM is given by x=10sin⁡(wt+π3)mx=10 \sin \left(w t+\frac{\pi}{3}\right) m. The time period of motion is 3.14 s3.14 \mathrm{~s}. The velocity of the particle at t=0t=0 is ______m/s\mathrm{m} / \mathrm{s}.JEE Main/Numerical/Medium/Simple Harmonic Motion
  17. 17A particle performs simple harmonic motion with amplitude AA. Its speed is increased to three times at an instant when its displacement is 2A3\dfrac{2A}{3}. The new amplitude of motion is nA3\dfrac{nA}{3}. The value of nn is _____.JEE Main/Numerical/Medium/Simple Harmonic Motion
  18. 18A simple harmonic oscillator has an amplitude AA and time period 6π6\pi second. Assuming the oscillation starts from its mean position, the time required by it to travel fromx=Ax=A to x=32Ax=\dfrac{\sqrt{3}}{2}A will be πxs\dfrac{\pi }{x}s, where x=_______.JEE Main/Numerical/Medium/Simple Harmonic Motion
  19. 19A particle executes simple harmonic motion with an amplitude of 4cm4cm. At the mean position, velocity of the particle is 10cms−110cm{s}^{-1}. The distance of the particle from the mean position when its speed becomes 5cms−15cm{s}^{-1} is αcm\sqrt{\alpha }cm, where α=\alpha =______.JEE Main/Numerical/Medium/Simple Harmonic Motion
  20. 20In a linear Simple Harmonic Motion (SHM)
    (A) Restoring force is directly proportional to the displacement.
    (B) The acceleration and displacement are opposite in direction.
    (C) The velocity is maximum at mean position.
    (D) The acceleration is minimum at extreme points.
    Choose the correct answer from the options given below:    JEE Main/MCQ/Medium/Simple Harmonic Motion
  21. 21For a periodic motion represented by the equation y=sinωt+cosωty=sin\omega t+cos\omega t the amplitude of the motion isJEE Main/MCQ/Medium/Simple Harmonic Motion
  22. 22For particle PP revolving round the centre OO with radius of circular path rr and regular velocity ω\omega, as shown in below figure, the projection of OPOP on the xx-axis at time tt is
    JEE Main/MCQ/Medium/Simple Harmonic Motion/With diagram
  23. 23A particle of mass 250g250g executes a simple harmonic motion under a periodic force F=(–25x)NF=(–25x)N. The particle attains a maximum speed of 4ms−14m{s}^{-1} during its oscillation. The amplitude of the motion is ______cmcm.JEE Main/Numerical/Medium/Simple Harmonic Motion
  24. 24A particle executes simple harmonic motion between x=–Aandx=+Ax=–A\text{and}x=+A. If time taken by particle to go from x=0x=0 to A2\dfrac{A}{2} is 2s2s; then time taken by particle in going from x=A2x=\dfrac{A}{2} to AA is:JEE Main/MCQ/Medium/Simple Harmonic Motion
  25. 25The potential energy of a particle of mass 4kg4kg in motion along the xx-axis is given by U=4(1−cos⁡4x)JU=4\left(1-\cos 4x\right)J. The time period of the particle for small oscillation (sin⁡θ≃θ)\left(\sin \theta ≃\theta \right) (πK)s\left(\dfrac{\pi }{K}\right)s. The value of KK is _____ .JEE Main/Numerical/Medium/Simple Harmonic Motion
  26. 26When a particle executes simple Harmonic motion, the nature of graph of velocity as function of displacement will beJEE Main/MCQ/Medium/Simple Harmonic Motion
  27. 27Two waves executing simple harmonic motion travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the 3\sqrt{3} times of amplitude of individual motions. The phase difference between the two motions is _____ (degree)JEE Main/Numerical/Medium/Simple Harmonic Motion
  28. 28The motion of a simple pendulum executing S.H.M. is represented by the following equation y=Asin⁡(πt+ϕ)y=A\sin \left(\pi t+\phi \right), where time is measured in second. The length of pendulum isJEE Main/MCQ/Medium/Simple Harmonic Motion
  29. 29A body is performing simple harmonic with an amplitude of 10cm10cm. The velocity of the body was tripled by air Jet when it is at 5cm5cm from its mean position. The new amplitude of vibration is xcm\sqrt{x}cm. The value of xx is _____ .JEE Main/Numerical/Medium/Simple Harmonic Motion
  30. 30A particle executes simple harmonic motion. Its amplitude is 8cm8cm and time period is 6s6s. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is _____ ssJEE Main/Numerical/Medium/Simple Harmonic Motion
  31. 31The equation of a particle executing simple harmonic motion is given by x=sin⁡π(t+13)mx=\sin \pi \left(t+\dfrac{1}{3}\right)m. At t=1st=1s, the speed of particle will be (Given: π=3.14\pi =3.14)JEE Main/MCQ/Medium/Simple Harmonic Motion
  32. 32Two massless springs with spring constants 2k2k and 9k9k, carry 50g50g and 100g100g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be :JEE Main/MCQ/Medium/Simple Harmonic Motion
  33. 33A bob of mass mm suspended by a thread of length ℓ\ell undergoes simple harmonic oscillations with time period T.T. If the bob is immersed in a liquid that has density 14\dfrac{1}{4} times that of the bob and the length of the thread is increased by (13)rd{\left(\dfrac{1}{3}\right)}^{rd} of the original length, then the time period of the simple harmonic oscillations will be:JEE Main/MCQ/Medium/Simple Harmonic Motion
  34. 34A particle of mass 1kg1kg is hanging from a spring of force constant 100Nm−1.100N{m}^{-1}. The mass is pulled slightly downward and released so that it executes free simple harmonic motion with time period T.T. The time when the kinetic energy and potential energy of the system will become equal, is Tn.\dfrac{T}{n}. The value of nn is ________.JEE Main/Numerical/Medium/Simple Harmonic Motion
  35. 35Two simple harmonic motion, are represented by the equations
    y1=10sin⁡(3πt+π3);y2=5(sin⁡3πt+3cos⁡3πt){y}_{1}=10\sin \left(3\pi t+\dfrac{\pi }{3}\right);{y}_{2}=5(\sin 3\pi t+\sqrt{3}\cos 3\pi t)
    Ratio of amplitude of     y1{y}_{1} to y2=x:1{y}_{2}=x:1. The value of xx is    JEE Main/Numerical/Medium/Simple Harmonic Motion
  36. 36Two simple harmonic motions are represented by the equations x1=5sin⁡(2πt+π4){x}_{1}=5\sin \left(2\pi t+\dfrac{\pi }{4}\right) and x2=52(sin⁡2πt+cos⁡2πt).{x}_{2}=5\sqrt{2}(\sin 2\pi t+\cos 2\pi t). The amplitude of the second motion is _____ times the amplitude in the first motion.JEE Main/Numerical/Medium/Simple Harmonic Motion
  37. 37A particle executes simple harmonic motion represented by displacement function as x(t)=Asin⁡(ωt+ϕ)x(t)=A\sin (\omega t+\phi ). If the position and velocity of the particle at t=0st=0s are 2cm2cm and 2ωcms−12\omega cm{s}^{-1} respectively, then its amplitude is x2cmx\sqrt{2}cm where the value of xx isJEE Main/Numerical/Medium/Simple Harmonic Motion
  38. 38An object of mass 0.5kg0.5kg is executing simple harmonic motion. It amplitude is 5cm5cm and time period (T) is 0.2s0.2s. What will be the potential energy of the object at an instant t=T4st=\dfrac{T}{4}s starting from mean position. Assume that the initial phase of the oscillation is zero.JEE Main/MCQ/Medium/Simple Harmonic Motion
  39. 39A particle starts executing simple harmonic motion (SHM)(SHM) of amplitude aa and total energy E.E. At any instant, its kinetic energy is 3E4\dfrac{3E}{4}, then its displacement yy is given by:JEE Main/MCQ/Medium/Simple Harmonic Motion
  40. 40A particle performs simple harmonic motion with a period of 22 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is 1as.\dfrac{1}{a}s. The value of aa to the nearest integer isJEE Main/Numerical/Medium/Simple Harmonic Motion
  41. 41A block of mass 1kg1kg attached to a spring is made to oscillate with an initial amplitude of 12cm12cm. After 22 minutes the amplitude decreases to 6cm6cm. Determine the value of the damping constant for this motion. (take ln⁡2=0.693\ln 2=0.693 )JEE Main/MCQ/Medium/Simple Harmonic Motion
  42. 42A particle executes S.H.M. with amplitude AA and time period TT. The displacement of the particle when its speed is half of maximum speed is xA2.\dfrac{\sqrt{x}A}{2}. The value of xx isJEE Main/Numerical/Medium/Simple Harmonic Motion
  43. 43A particle executes S.H.M., the graph of velocity as a function of displacement is :JEE Main/MCQ/Medium/Simple Harmonic Motion
  44. 44Y=Asin⁡(ωt+ϕ0)Y=A\sin \left(\omega t+{\phi }_{0}\right) is the time-displacement equation of a SHM.SHM. At t=0t=0 the displacement of the particle is Y=A2Y=\dfrac{A}{2} and it is moving along negative xx-direction. Then the initial phase angle ϕ0{\phi }_{0} will be:JEE Main/MCQ/Medium/Simple Harmonic Motion
  45. 45The point AA moves with a uniform speed along the circumference of a circle of radius 0.36m0.36m and covers 30∘30^{\circ} in 0.1s0.1s. The perpendicular projection PP from AA on the diameter MNMN represents the simple harmonic motion of PP. The restoration force per unit mass when PP touches MM will be :
    JEE Main/MCQ/Medium/Simple Harmonic Motion/With diagram
  46. 46When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is:JEE Main/MCQ/Medium/Simple Harmonic Motion
  47. 47A damped harmonic oscillator has a frequency of 55 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to 11000\dfrac{1}{1000} of the original amplitude is close to:JEE Main/MCQ/Medium/Simple Harmonic Motion
  48. 48An oscillator of mass MM is at rest in its equilibrium position in a potential, V=12k(x–X)2V=\dfrac{1}{2}k{\left(x–X\right)}^{2} . A particle of mass mm comes from the right with speed uu and collides completely inelastic with MM and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after 1313 collisions is: (M=10,m=5,u=1,k=1)\left(M=10,m=5,u=1,k=1\right)JEE Main/MCQ/Medium/Simple Harmonic Motion
  49. 49Two simple harmonic motions, as shown, are at right angles. They are combined to form Lissajous figures.
    x(t)=Asin⁡(at+δ)x(t)=A \sin (a t+\delta)
    y(t)=Bsin⁡(bt)y(t)=B \sin (b t)
    Identify the correct match below    JEE Main/MCQ/Medium/Simple Harmonic Motion
  50. 50The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10s−1.10{s}^{-1}. At, t=0t=0 the displacement is 5m.5m. What is the maximum acceleration? The initial phase is π4\dfrac{\pi }{4} .JEE Main/MCQ/Medium/Simple Harmonic Motion
  51. 51Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to AA and TT, respectively. At time t=0t=0 one particle has displacement AA while the other one has displacement −A2-\dfrac{A}{2} and they are moving towards each other. If they cross each other at time tt, then tt is:JEE Main/MCQ/Medium/Simple Harmonic Motion
  52. 52A particle performs simple harmonic motion with amplitude A. Its speed is tripled at the instant that it is at a distance 2A3\dfrac{2A}{3} from equilibrium position. The new amplitude of the motion is:JEE Main/MCQ/Medium/Simple Harmonic Motion
  53. 53A simple harmonic oscillator of angular frequency 2rads−12rad{s}^{-1} is acted upon by an external force F=sin⁡⁡tN.F=\sin ⁡tN.If the oscillator is at rest in its equilibrium position at t=0,t=0, its position at later times is proportional to:JEE Main/MCQ/Medium/Simple Harmonic Motion
  54. 54xandyxandy displacements of a particle are given as x(t)=asin⁡⁡ωtandy(t)=asin⁡⁡2ωt.x\left(t\right)=a\sin ⁡\omega tandy\left(t\right)=a\sin ⁡2\omega t. Its trajectory will look like:JEE Main/MCQ/Medium/Simple Harmonic Motion
  55. 55A body is in simple harmonic motion with time period T=0.5sT=0.5 \text{s} and amplitude A=1cmA=1 \text{cm}. Find the average velocity in the interval in which it moves from equilibrium position to half of its amplitude.JEE Main/MCQ/Medium/Simple Harmonic Motion
  56. 56Which of the following expressions corresponds to simple harmonic motion along a straight line, where x\mathrm{x} is the displacement and a,b,c\mathrm{a}, \mathrm{b}, \mathrm{c} are positive constants?JEE Main/MCQ/Medium/Simple Harmonic Motion
  57. 57A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; x=a1cos⁡⁡ωtx={a}_{1}\cos ⁡\omega t and y=a2cos⁡⁡2ωty={a}_{2}\cos ⁡2\omega t traces a curve given by :JEE Main/MCQ/Medium/Simple Harmonic Motion
  58. 58A particle moves with simple harmonic motion in a straight line. In first τs\tau s, after starting from rest it travels a distance a, and in next τs\tau s it travels 2a, in same direction, then :JEE Main/MCQ/Medium/Simple Harmonic Motion
  59. 59A mass m=1.0 kgm=1.0 \mathrm{~kg} is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is 500 N/m500 \mathrm{~N} / \mathrm{m}. What is the amplitude A of the motion, so that the mass mm tends to get detached from the pan ? (Take g=10 m/s2g=10 \mathrm{~m} / \mathrm{s}^2 ).
    The spring is stiff enough so that it does not get distorted during the motion.
    JEE Main/MCQ/Medium/Simple Harmonic Motion/With diagram
  60. 60Two simple pendulums of length 1 m1 \mathrm{~m} and 4 m4 \mathrm{~m} respectively are both given small displacement in the same direction at the same instant. They will be again in phase after the shorter pendulum has completed number of oscillations equal to:JEE Main/MCQ/Medium/Simple Harmonic Motion
  61. 61The displacement y(t)=Asin⁡(ωt+ϕ)y(t)=A \sin (\omega t+\phi) of a pendulum for ϕ=2π3\phi=\frac{2 \pi}{3} is correctly represented byJEE Main/MCQ/Medium/Simple Harmonic Motion
  62. 62A mass MM, attached to a horizontal spring, executes S.H.M. with amplitude A1A_1. When the mass MM passes through its mean position then a smaller mass m\mathrm{m} is placed over it and both of them move together with amplitude A2A_2. The ratio of (A1A2)\left(\frac{A_1}{A_2}\right) is :JEE Main/MCQ/Medium/Simple Harmonic Motion
  63. 63Two particles are executing simple harmonic motion of the same amplitude A\mathrm{A} and frequency ω\omega along the xx-axis. Their mean position is separated by distance X0(X0>A)X_0\left(X_0\gt A\right). If the maximum separation between them is (X0+A)\left(X_0+A\right), the phase difference between their motion is :JEE Main/MCQ/Medium/Simple Harmonic Motion
  64. 64If x,vx, v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T\mathrm{T}, then, which of the following does not change with time?JEE Main/MCQ/Medium/Simple Harmonic Motion
  65. 65A point mass oscillates along the xx-axis according to the law x=x0cos⁡(ωt−π/4)\mathrm{x=x_0 \cos (\omega t-\pi / 4)}. If the acceleration of the particle is written as
    a=Acos⁡(ωt+δ)\mathrm{a=A \cos (\omega t+\delta)}    JEE Main/MCQ/Medium/Simple Harmonic Motion
  66. 66The displacement of an object attached to a spring and executing simple harmonic motion is given by x=2×10−2cos⁡πtx=2 \times 10^{-2} \cos \pi t metres. The time at which the maximum speed first occurs isJEE Main/MCQ/Medium/Simple Harmonic Motion
  67. 67A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω\omega. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first timeJEE Main/MCQ/Medium/Simple Harmonic Motion
  68. 68Two simple harmonic motions are represented by the equation y1=0.1\mathrm{y}_1=0.1 sin⁡(100πt+π3)\sin \left(100 \pi t+\frac{\pi}{3}\right) and y2=0.1cos⁡πty_2=0.1 \cos \pi t. The phase difference of the velocity of particle 1 w.r.t. the velocity of the particle 2 isJEE Main/MCQ/Medium/Simple Harmonic Motion
  69. 69The function sin⁡2(ωt)\sin ^2(\omega t) representsJEE Main/MCQ/Medium/Simple Harmonic Motion
  70. 70The displacement of a particle varies according to the relation x=4(cos⁡πt+sin⁡πt)x=4(\cos \pi t+\sin \pi t). The amplitude of the particle isJEE Main/MCQ/Medium/Simple Harmonic Motion
  71. 71Two particles A\mathrm{A} and B\mathrm{B} of equal masses are suspended from two massless springs of spring constant k1\mathrm{k}_1 and k2\mathrm{k}_2, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of AA and BB isJEE Main/MCQ/Medium/Simple Harmonic Motion
  72. 72The displacement of a particle, executing simple harmonic motion with time period TT, is expressed as x(t)=Asin⁡ωtx(t)=A \sin \omega t, where AA is the amplitude. The maximum value of potential energy of this oscillator is found at t=T/2βt=T / 2 \beta. The value of β\beta is ____\_\_\_\_.JEE Main/Numerical/Medium/Energy of Simple Harmonic Motion
  73. 73Two blocks with masses 100 g and 200 g are attached to the ends of springs AA and BB as shown in figure. The energy stored in AA is EE. The energy stored in BB, when spring constants kA,kBk_{A}, k_{B} of AA and BB, respectively satisfy the relation 4kA=3kB′4 k_{A}=3 k_{B^{\prime}}, is :
    JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion/With diagram
  74. 74The kinetic energy of a simple harmonic oscillator is oscillating with angular frequency of 176rad/s176 \mathrm{rad} / \mathrm{s}. The frequency of this simple harmonic oscillator is ____\_\_\_\_ Hz. [\left[\right. take π=227]\left.\pi=\frac{22}{7}\right]JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  75. 75A particle oscillates along the xx-axis according to the law, x(t)=x0sin⁡2(t2)x(\mathrm{t})=x_0 \sin ^2\left(\frac{\mathrm{t}}{2}\right) where x0=1 mx_0=1 \mathrm{~m}. The kinetic energy (K)(\mathrm{K}) of the particle as a function of xx is correctly represented by the graphJEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  76. 76When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is x8\dfrac{x}{8}, where x=x=_________.JEE Main/Numerical/Medium/Energy of Simple Harmonic Motion
  77. 77A particle executes SHM of amplitudeAA. The distance from the mean position when its kinetic energy becomes equal to its potential energy is:JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  78. 78At a given point of time the value of displacement of a simple harmonic oscillator is given as y=Acos⁡(30∘).y=A\cos \left(30^{\circ}\right). If amplitude is 40cm40cm and kinetic energy at that time is 200J,200J, the value of force constant 1.0×10xNm–11.0\times {10}^{x}N{m}^{–1}. The value of xx is _____.JEE Main/Numerical/Medium/Energy of Simple Harmonic Motion
  79. 79Which graph represents the difference between total energy and potential energy of a particle executing SHMSHM vs its distance from mean position?JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  80. 80A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will beJEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  81. 81The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement (xx) starting from mean position to extreme position (AA) is given byJEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  82. 82A simple pendulum with length 100cm100cm and bob of mass 250g250g is executing S.H.M of amplitude 10cm10cm. The maximum tension in the string is found to be x40N\dfrac{x}{40}N. The value of xx is _____.JEE Main/Numerical/Medium/Energy of Simple Harmonic Motion
  83. 83The amplitude of a particle executing SHM is 3cm3cm. The displacement at which its kinetic energy will be 2525% more than the potential energy is: ______ cmcm.JEE Main/Numerical/Medium/Energy of Simple Harmonic Motion
  84. 84The general displacement of a simple harmonic oscillator is x=Asin⁡ωtx=A\sin \omega t. Let TT be its time period. The slope of its potential energy (UU) – time (tt) curve will be maximum when t=Tβt=\dfrac{T}{\beta }. The value of β\beta is ______.JEE Main/Numerical/Medium/Energy of Simple Harmonic Motion
  85. 85A mass 0.9kg0.9kg, attached to a horizontal spring, executes SHM with an amplitude A1{A}_{1}. When this mass passes through its mean position, then a smaller mass of 124g124g is placed over it and both masses move together with amplitude A2{A}_{2}. If the ratio A1A2\dfrac{{A}_{1}}{{A}_{2}} is αα−1\dfrac{\alpha }{\alpha -1}, then the value of α\alpha will be _____ .JEE Main/Numerical/Medium/Energy of Simple Harmonic Motion
  86. 86A mass of 5kg5kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4m4m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed ?
    JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion/With diagram
  87. 87For a body executing S.H.M. :
    (a) Potential energy is always equal to its     K.E.K.E.
    (b) Average potential and kinetic energy over any given time interval are always equal.
    (c) Sum of the kinetic and potential energy at any point of time is constant.
    (d) Average     K.E.K.E. in one time period is equal to average potential energy in one time period.
    Choose the most appropriate option from the options given below :    JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  88. 88The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.

    The potential energy     U(x)U(x) versus time (t)\left(t\right) plot of the particle is correctly shown in figure:    JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion/With diagram
  89. 89In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  90. 90For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  91. 91A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become ƒA. The value of ƒ is:JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  92. 92The displacement time graph of a particle executing SHM is given in figure: (sketch is schematic and not to scale)

    Which of the following statements is/are true for this motion?
    (A) The force is zero at     t=3T4t=\dfrac{3T}{4}
    (B) The magnitude of acceleration is maximum at     t=Tt=T
    (C) The speed is maximum at     t=T4t=\dfrac{T}{4}
    (D) The     P.E.P.E. is equal to K.E.K.E. of the oscillation at t=T2t=\dfrac{T}{2}    JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion/With diagram
  93. 93A pendulum is executing simple harmonic motion and its maximum kinetic energy is K1\mathrm{K}_{1}. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is K2\mathrm{K}_{2}JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  94. 94A particle undergoing simple harmonic motion has time

    dependent displacement given by     x(t)=Asin⁡πt90x(t)=\mathrm{A} \sin \frac{\pi t}{90}. The ratio of kinetic to potential energy of this particle at t=210 s\mathrm{t}=210 \mathrm{~s} will be    JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  95. 95A particle is executing simple harmonic motion (SHM)(SHM) of amplitude A,A, along the xx -axis, about x=0.x=0. When its potential Energy (PE)\left(PE\right) equal kinetic energy (KE),\left(KE\right), the position of the particle will be:JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  96. 96A body of mass MM and charge qq is connected to a spring of spring constant kk. It is oscillating along xx-direction about its equilibrium position in the horizontal plane, taken to be at x=0x=0, with an amplitude AA. An electric field EE is applied along the xx-direction. Which of the following statements is correct?JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  97. 97A particle is executing simple harmonic motion with a time period TT. At time t=0t=0, it is at its position of equilibrium. The kinetic energy - time graph of the particle will look like:JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  98. 98For a simple pendulum, a graph is plotted between its kinetic energy (K.E.) and potential energy (P.E.) against its displacement d. which one of the following represents these correctly? (graphs are schematic and not drawn to scale)JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  99. 99A particle of mass mm executes simple harmonic motion with amplitude ' aa ' and frequency ' vv '. The average kinetic energy during its motion from the position of equilibrium to the end isJEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  100. 100Starting from the origin, a body oscillates simple harmonically with a period of 2 s2 \mathrm{~s}. After what time will its kinetic energy be 75%75 \% of the total energy?JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  101. 101The total energy of particle, executing simple harmonic motion isJEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  102. 102A body executes simple harmonic motion. The potential energy (P.E), the kinetic energy (K.E) and total energy (T.E) are measured as a function of displacement xx. Which of the following statements is true?JEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  103. 103In a simple harmonic oscillator, at the mean positionJEE Main/MCQ/Medium/Energy of Simple Harmonic Motion
  104. 104A spring stretches by 22 mm when it is loaded with a mass of 200200 g. From equilibrium position the mass is further pulled down by 22 mm and released. The frequency associated with the system and maximum energy in the spring are __________ Hz and __________ J, respectively. (Take g =10= 10 m/s2^2)JEE Main/MCQ/Medium/Time Period and Frequency
  105. 105The time period of a simple harmonic oscillator is T=2πkmT=2 \pi \sqrt{\frac{k}{m}}. Measured value of mass (m)(m) of the object is 10 g with an accuracy of 10 mg and time for 50 oscillations of the spring is found to be 60 s using a watch of 2 s resolution. Percentage error in determination of spring constant (k)(k) is ____\_\_\_\_ \%.JEE Main/MCQ/Medium/Time Period and Frequency
  106. 106Two blocks of masses mm and M,(M>m)M,(M \gt m), are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released then
    (    μ=\mu= coefficient of friction between the two blocks)

    (A) The time period of small oscillation of the two blocks is     T=2π( m+M)k\mathrm{T}=2 \pi \sqrt{\frac{(\mathrm{~m}+\mathrm{M})}{\mathrm{k}}}
    (B) The acceleration of the blocks is     a=kxM+m\mathrm{a}=\frac{\mathrm{kx}}{\mathrm{M}+\mathrm{m}} (x=\mathrm{x}= displacement of the blocks from the mean position)
    (C) The magnitude of the frictional force on the upper block is     mμ∣x∣M+m\frac{m \mu|x|}{M+m}
    (D) The maximum amplitude of the upper block, if it does not slip, is     μ(M+m)gk\frac{\mu(M+m) g}{k}
    (E) Maximum frictional force can be     μ(M+m)g\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}.
    Choose the correct answer from the options given below:    JEE Main/MCQ/Medium/Time Period and Frequency/With diagram
  107. 107Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A) : Knowing initial position     x0x_0 and initial momentum p0p_0 is enough to determine the position and momentum at any time tt for a simple harmonic motion with a given angular frequency ω\omega.
    Reason (R): The amplitude and phase can be expressed in terms of     x0x_0 and p0\mathrm{p}_0.
    In the light of the above statements, choose the correct answer from the options given below :    JEE Main/MCQ/Medium/Time Period and Frequency
  108. 108Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.
    Reason (R): The mass of the pendulum remains unchanged at Earth and the other planet.
    In the light of the above statements, choose the correct answer from the options given below :    JEE Main/MCQ/Medium/Time Period and Frequency
  109. 109A particle of mass 0.50 kg0.50 \mathrm{~kg} executes simple harmonic motion under force F=−50(Nm−1)xF=-50\left(\mathrm{Nm}^{-1}\right) x. The time period of oscillation is x35 s\frac{x}{35} \mathrm{~s}. The value of xx is _______
    (Given     π=227\pi=\frac{22}{7} )    JEE Main/Numerical/Medium/Time Period and Frequency
  110. 110A mass mm is suspended from a spring of negligible mass and the system oscillates with a frequency f1.{f}_{1}. The frequency of oscillations if a mass 9m9m is suspended from the same spring is f2.{f}_{2}. The value of f1f2\dfrac{{f}_{1}}{{f}_{2}} is _____ .JEE Main/Numerical/Medium/Time Period and Frequency
  111. 111A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4m4m, then the time period of small oscillations will be _________ss.
    [[take g=π2ms−2g={\pi }^{2}m{s}^{-2}]    JEE Main/Numerical/Medium/Time Period and Frequency
  112. 112A particle executes S.H.M. of amplitude AA along xx-axis. At t=0t=0, the position of the particle is x=A2x=\dfrac{A}{2} and it moves along positive xx-axis. The displacement of particle in time tt is x=Asin⁡(ωt+δ)x=A\sin \left(\omega t+\delta \right), then the value δ\delta will beJEE Main/MCQ/Medium/Time Period and Frequency
  113. 113Choose the correct length (L)(L) versus square of time period (T2)({T}_{2}) ) graph for a simple pendulum executing simple harmonic motion.JEE Main/MCQ/Medium/Time Period and Frequency
  114. 114The velocity of a particle executing SHM varies with displacement (xx) as 4v2=50–x24{v}^{2}=50–{x}^{2}. The time period of oscillations is x7s\dfrac{x}{7}s. The value of xx is ______.
    [Take     π=227\pi =\dfrac{22}{7}]    JEE Main/Numerical/Medium/Time Period and Frequency
  115. 115A mass mm attached to free end of a spring executes SHM with a period of 1s1s. If the mass is increased by 3kg3kg the period of oscillation increases by one second, the value of mass mm is ________ kgkg.JEE Main/Numerical/Medium/Time Period and Frequency
  116. 116A block of mass 2kg2kg is attached with two identical springs of spring constant 20Nm−120N{m}^{-1} each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is πX\dfrac{\pi }{\sqrt{X}} in SI unit. The value of XX is______.
    JEE Main/Numerical/Medium/Time Period and Frequency/With diagram
  117. 117The metallic bob of simple pendulum has the relative density 55. The time period of this pendulum is 10s10s. If the metallic bob is immersed in water, then the new time period becomes 5xs5\sqrt{x}s. The value of xx will be _____ .JEE Main/Numerical/Medium/Time Period and Frequency
  118. 118The time period of oscillation of a simple pendulum of length LL suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination α\alpha, is given by :JEE Main/MCQ/Medium/Time Period and Frequency
  119. 119As per given figures, two springs of spring constants KK and 2K2K are connected to mass mm. If the period of oscillation in figure (a) is 3s3s, then the period of oscillation in figure (b) will be xs\sqrt{x}s. The value of xx is _____ .
    JEE Main/Numerical/Medium/Time Period and Frequency/With diagram
  120. 120The displacement of simple harmonic oscillator after 33 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion isJEE Main/MCQ/Medium/Time Period and Frequency
  121. 121Time period of a simple pendulum in a stationary lift is TT. If the lift accelerates with g6\dfrac{g}{6} vertically upwards then the time period will be
    (Where     g=g= acceleration due to gravity)    JEE Main/MCQ/Medium/Time Period and Frequency
  122. 122T0{T}_{0} is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to 116\dfrac{1}{16} times of its initial value, the modified time period isJEE Main/MCQ/Medium/Time Period and Frequency
  123. 123A particle is making simple harmonic motion along the XX-axis. If at a distances x1{x}_{1} and x2{x}_{2} from the mean position the velocities of the particle are v1{v}_{1} and v2{v}_{2}, respectively. The time period of its oscillation is given as:JEE Main/MCQ/Medium/Time Period and Frequency
  124. 124Time period of a simple pendulum is TT inside a lift when the lift is stationary. If the lift moves upwards with an acceleration g2\dfrac{g}{2}, the time period of pendulum will be :JEE Main/MCQ/Medium/Time Period and Frequency
  125. 125If the time period of a two meter long simple pendulum is 2s2s, the acceleration due to gravity at the place where pendulum is executing S.H.M. is:JEE Main/MCQ/Medium/Time Period and Frequency
  126. 126In the given figure, a body of mass MM is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant k,k, the frequency of oscillation of given body is:
    JEE Main/MCQ/Medium/Time Period and Frequency/With diagram
  127. 127An object of mass mm is suspended at the end of a massless wire of length LL and area of cross-section, A. Young modulus of the material of the wire is YY. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is :JEE Main/MCQ/Medium/Time Period and Frequency
  128. 128A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period T1{T}_{1} and (ii) back and forth in a direction perpendicular to its plane, with a period T2{T}_{2}. The ratio T1T2\dfrac{{T}_{1}}{{T}_{2}} will be :JEE Main/MCQ/Medium/Time Period and Frequency
  129. 129A simple pendulum oscillating in air has period TT . The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is 116th\dfrac{1}{16}th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is:JEE Main/MCQ/Medium/Time Period and Frequency
  130. 130A simple harmonic motion is represented by:
    y=5(sin⁡3πt+3cos⁡3πt)cmy=5\left(\sin 3\pi t+\sqrt{3}\cos 3\pi t\right)cm
    The amplitude and time period of the motion are:    JEE Main/MCQ/Medium/Time Period and Frequency
  131. 131A simple pendulum of length 1 m1 \mathrm{~m} is oscillating with an angular frequency 10rad/s10 \mathrm{rad} / \mathrm{s}. The support of the pendulum starts oscillating up and down with a small angular frequency of 1rad/s1 \mathrm{rad} / \mathrm{s} and an amplitude of 10−2 m10^{-2} \mathrm{~m}. The relative change in the angular frequency of the pendulum is best given by :JEE Main/MCQ/Medium/Time Period and Frequency
  132. 132A cylindrical plastic bottle of negligible mass is filled with 310ml310 ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency ω.\omega . If the radius of the bottle is 2.5cm2.5 cm then ω\omega is close to: (( density of water =103kg/m3)={10}^{3}kg/{m}^{3})JEE Main/MCQ/Medium/Time Period and Frequency
  133. 133A particle executes simple harmonic motion with an amplitude of 5cm5cm . When the particle is at 4cm4cm from the mean position, the magnitude of its velocity in SISI units is equal to that of its acceleration. Then, its periodic time in seconds is:JEE Main/MCQ/Medium/Time Period and Frequency
  134. 134A hoop and a solid cylinder of same mass and radius are made of a permanent magnetic material with their respective axes. But the magnetic moment of hoop is twice of solid cylinder. They are placed in a uniform magnetic field in such a manner that their magnetic moments make a small angle with the field. If the oscillation periods of hoop and cylinder are Th{T}_{h} and Tc{T}_{c} respectively, then:JEE Main/MCQ/Medium/Time Period and Frequency
  135. 135A particle executes simple harmonic motion and it is located at x=a,bx=a,b and cc at time t0,2t0and3t0{t}_{0},2{t}_{0}and3{t}_{0} respectively. The frequency of the oscillation is:JEE Main/MCQ/Medium/Time Period and Frequency
  136. 136A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012s−1{10}^{12}{s}^{-1} . What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver,=108gmol−1=108g{mol}^{-1} and Avogadro number =6.02×1023=6.02\times {10}^{23})JEE Main/MCQ/Medium/Time Period and Frequency
  137. 137In an engine the piston undergoes vertical simple harmonic motion with amplitude 7cm. A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to :JEE Main/MCQ/Medium/Time Period and Frequency
  138. 138The amplitude of a simple pendulum, oscillating in air with a small spherical bob, decreases from 10 cm to 8 cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3, the time in which amplitude of this pendulum will reduce from 10 cm to 5 cm in carbondioxide will be close to (ln 5 = 1.601, ln 2 = 0.693).JEE Main/MCQ/Medium/Time Period and Frequency
  139. 139An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M\text{M}. The piston and the cylinder have equal cross-sectional area A\text{A}. When the piston is in equilibrium, the volume of the gas is V0{V}_{0} and its pressure is M0{M}_{0}. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
    [Assume the system is in space.]    JEE Main/MCQ/Medium/Time Period and Frequency
  140. 140The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7 mm7 \mathrm{~mm}, is 4.4 m/s4.4 \mathrm{~m} / \mathrm{s}. The period of oscillation isJEE Main/MCQ/Medium/Time Period and Frequency
  141. 141If a simple harmonic motion is represented by d2xdt2+αx=0\frac{\mathrm{d}^2 \mathrm{x}}{\mathrm{dt}^2}+\alpha \mathrm{x}=0, its time period isJEE Main/MCQ/Medium/Time Period and Frequency
  142. 142A particle at the end of a spring executes simple harmonic motion with a period t1t_1, while the corresponding period for another spring is t2t_2. If the period of oscillation with the two springs in series is t\mathrm{t}, thenJEE Main/MCQ/Medium/Time Period and Frequency
  143. 143The bob of a simple pendulum executes simple harmonic motion in water with a period tt, while the period of oscillation of the bob is t0t_0 in air. Neglecting frictional force of water and given that the density of the bob is (43)×1000 kg/m3\left(\frac{4}{3}\right) \times 1000 \mathrm{~kg} / \mathrm{m}^3. What relationship between tt and t0t_0 is true?JEE Main/MCQ/Medium/Time Period and Frequency
  144. 144A mass M\mathrm{M} is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T. If the mass is increased by m\mathrm{m}, the time period becomes 5 T3\frac{5 \mathrm{~T}}{3}. Then the ratio of mM\frac{\mathrm{m}}{\mathrm{M}} isJEE Main/MCQ/Medium/Time Period and Frequency
  145. 145A child swinging on a swing in sitting position, stands up, then the time period of the swing willJEE Main/MCQ/Medium/Time Period and Frequency
  146. 146The frequency of oscillation of a mass mm suspended by a spring is v1v_1. If the length of the spring is cut to half, the same mass oscillates with frequency v2v_2. The value of v2/v1v_2/v_1 is ________.JEE Main/MCQ/Medium/Applications of SHM
  147. 147A uniform disc of radius RR and mass MM is free to oscillate about the axis AA as shown in the figure. For small oscillations the time period is ______.
    (    gg is acceleration due to gravity)
    JEE Main/MCQ/Medium/Applications of SHM/With diagram
  148. 148A simple pendulum of string length 30 cm performs 20 oscillations in 10 s. The length of the string required for the pendulum to perform 40 oscillations in the same time duration is ____\_\_\_\_ cm. [Assume that the mass of the pendulum remains same.]JEE Main/MCQ/Medium/Applications of SHM
  149. 149Using a simple pendulum experiment gg is determind by measuring its time period TT. Which of the following plots represent the correct relation between the pendulum length LL and time period TT ?JEE Main/MCQ/Medium/Applications of SHM
  150. 150Two simple pendulums having lengths l1l_1 and l2l_2 with negligible string mass undergo angular displacements θ1\theta_1 and θ2\theta_2, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?JEE Main/MCQ/Medium/Applications of SHM
  151. 151Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
    Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.
    Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.
    In the light of the above statements, choose the most appropriate answer from the options given below :    JEE Main/MCQ/Medium/Applications of SHM
  152. 152A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is yπ×10−2 sy \pi \times 10^{-2} \mathrm{~s}, where the value of yy is
    (Acceleration due to gravity,     g=10 m/s2g=10 \mathrm{~m} / \mathrm{s}^2, density of water =103 kg/m3=10^3 \mathrm{~kg} / \mathrm{m}^3 )    JEE Main/MCQ/Medium/Applications of SHM
  153. 153In simple harmonic motion, the total mechanical energy of given system is EE. If mass of oscillating particle PP is doubled then the new energy of the system for same amplitude is:
    JEE Main/MCQ/Medium/Applications of SHM/With diagram
  154. 154The time period of simple harmonic motion of mass MM in the given figure is παM5K\pi \sqrt{\dfrac{\alpha M}{5K}}, where the value of α\alpha is _______.JEE Main/Numerical/Medium/Applications of SHM/With diagram
  155. 155A rectangular block of mass 5kg5kg attached to a horizontal spiral spring executes simple harmonic motion of amplitude 1m1m and time period 3.14s3.14s. The maximum force exerted by spring on block is ___ NN.JEE Main/Numerical/Medium/Applications of SHM
  156. 156In the figure given below. a block of mass M=490gM=490g placed on a frictionless table is connected with two springs having same spring constant (K=2Nm−1K=2N{m}^{-1}). If the block is horizontally displaced through XX mm then the number of complete oscillations it will make in 14π14\pi seconds will be ______.
    JEE Main/Numerical/Medium/Applications of SHM/With diagram
  157. 157The maximum potential energy of a block executing simple harmonic motion is 25J25J. A is amplitude of oscillation. At A2\dfrac{A}{2}, the kinetic energy of the block isJEE Main/MCQ/Medium/Applications of SHM
  158. 158For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is 1kg1kg, the angular frequency is ω1{\omega }_{1}. When the mass block is 2kg2kg the angular frequency is ω2{\omega }_{2}. The ratio ω2ω1\dfrac{{\omega }_{2}}{{\omega }_{1}} is :
    JEE Main/MCQ/Medium/Applications of SHM/With diagram
  159. 159In figure (A), mass 2m2m is fixed on mass mm which is attached to two springs of spring constant kk. In figure (B), mass mm is attached to two spring of spring constant kk and 2k2k. If mass mm in (A) and (B) are displaced by distance xx horizontally and then released, then time period T1{T}_{1} and T2{T}_{2} corresponding to (A) and (B) respectively follow the relation.
    JEE Main/MCQ/Medium/Applications of SHM/With diagram
  160. 160Two identical tennis balls each having mass mm and charge qq are suspended from a fixed point by threads of length l.l. What is the equilibrium separation when each thread makes a small angle θ\theta with the vertical?JEE Main/MCQ/Medium/Applications of SHM
  161. 161A pendulum bob has a speed of 3ms−13m{s}^{-1} at its lowest position. The pendulum is 50cm50cm long. The speed of bob, when the length makes an angle of 60∘60^{\circ} to the vertical will be (g=10ms−2)\left(g=10m{s}^{-2}\right) ______ ms−1m{s}^{-1}.JEE Main/Numerical/Medium/Applications of SHM
  162. 162In the reported figure, two bodies AandBAandB of masses 200g200g and 800g800g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be _______ rads−1rad{s}^{-1} when k=20Nm−1k=20N{m}^{-{1}^{}}.
    JEE Main/Numerical/Medium/Applications of SHM/With diagram
  163. 163Two particles AA and BB of equal masses are suspended from two massless springs of spring constants K1{K}_{1} and K2{K}_{2} respectively.If the maximum velocities during oscillations are equal, the ratio of the amplitude of AA and BB isJEE Main/MCQ/Medium/Applications of SHM
  164. 164Consider two identical springs each of spring constant kk and negligible mass compared to the mass MM as shown. Fig. 11 shows one of them and Fig. 22 shows their series combination. The ratios of time period of oscillation of the two SHM is TbTa=x,\dfrac{{T}_{b}}{{T}_{a}}=\sqrt{x}, where value of xx is ______.
    (Round off to the Nearest Integer)
    JEE Main/Numerical/Medium/Applications of SHM/With diagram
  165. 165The amplitude of a mass-spring system, which is executing simple harmonic motion decreases with time. If mass =500g=500g, Decay constant =20gs−1=20g{s}^{-1} then how much time is required for the amplitude of the system to drop to half of its initial value? (ln⁡2=0.693)\left(\ln 2=0.693\right)JEE Main/MCQ/Medium/Applications of SHM
  166. 166Time period of a simple pendulum is TT. The time taken to complete 58\dfrac{5}{8} oscillations starting from mean position is α12T\dfrac{\alpha }{12}T. The value of α\alpha is ______.JEE Main/Numerical/Medium/Applications of SHM
  167. 167Given below are two statements:
    Statement     II: A second's pendulum has a time period of 11 second.
    Statement     IIII: It takes precisely one second to move between the two extreme positions. In the light of the above statements,
    choose the correct answer from the options given below    JEE Main/MCQ/Medium/Applications of SHM
  168. 168Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance R2\dfrac{R}{2} from the earth's centre, where RR is the radius of the earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period:JEE Main/MCQ/Medium/Applications of SHM
  169. 169Two identical springs of spring constant 2k2k are attached to a block of mass mm and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is :
    JEE Main/MCQ/Medium/Applications of SHM/With diagram
  170. 170In the given figure, a mass MM is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k.k. The mass oscillates on a frictionless surface with time period TT and amplitude A.A. When the mass is in equilibrium position, as shown in the figure, another mass mm is gently fixed upon it. The new amplitude of oscillation will be:
    JEE Main/MCQ/Medium/Applications of SHM/With diagram
  171. 171When a particle of mass mm is attached to a vertical spring of spring constant kk and released, its motion, is described by y(t)=y0sin⁡2ωty\left(t\right)={y}_{0}{\sin }^{2}\omega t, where 'yy' is measured from the lower end of upstretched spring. Then ω\omega is :JEE Main/MCQ/Medium/Applications of SHM
  172. 172The displacement of a damped harmonic oscillator is given by x(t)=e−0.1tcos⁡⁡(10πt+ϕ).x\left(t\right)={e}^{-0.1t}\cos ⁡\left(10\pi t+\phi \right). Here tt is in seconds. The time taken for its amplitude of vibration to drop to half of its initial value is close to:JEE Main/MCQ/Medium/Applications of SHM
  173. 173In an experiment to determine the period of a simple pendulum of length 1m1m, it is attached to different spherical bobs of radii r1{r}_{1} and r2{r}_{2} . The two spherical bobs have uniform mass distribution. If the relative difference in the periods, is found to be 5×10−4s5\times {10}^{-4}s, the difference in radii, ∣r1−r2∣\left|{r}_{1}-{r}_{2}\right| is best-given byJEE Main/MCQ/Medium/Applications of SHM
  174. 174A block of mass 0.1kg0.1kg is connected to an elastic spring of spring constant 640Nm−1640N{m}^{-1} and oscillates in a damping medium of damping constant 10−2kgs−1{10}^{-2}kg{s}^{-1} . The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to-JEE Main/MCQ/Medium/Applications of SHM
  175. 175A 1kg1kg block attached to a spring vibrates with a frequency of 1Hz1Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to a8kg8kgblock placed on the same table. So, the frequency of vibration of the 8kg8kg block isJEE Main/MCQ/Medium/Applications of SHM
  176. 176A cylindrical block of wood (density = 650kgm−3650kg{m}^{-3}), of base area 30cm230{cm}^{2} and height 54cm54cm, floats in a liquid of density 900kgm−3900kg{m}^{-3}. The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly) :JEE Main/MCQ/Medium/Applications of SHM
  177. 177A pendulum with the time period of 1s1s is losing energy due to damping. At a certain time, its energy is 45J45J. If after completing 1515 oscillations its energy has become 15J15J, then its damping constant (in s−1{s}^{-1}) will beJEE Main/MCQ/Medium/Applications of SHM
  178. 178Two bodies of masses 1kg1kg and 4kg4kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25rads−125rad{s}^{-1}, and amplitude 1.6cm1.6cm while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take g=10ms−2g=10m{s}^{-2}).
    JEE Main/MCQ/Medium/Applications of SHM/With diagram
  179. 179A uniform cylinder of length L\mathrm{L} and mass MM having cross-sectional area A\mathrm{A} is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density σ\sigma at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period T\mathrm{T} of the oscillations of the cylinder will be :JEE Main/MCQ/Medium/Applications of SHM
  180. 180Two charges, each equal to q\text{q}, are kept at x=−a\text{x}=-\text{a} and x=a\text{x}=\text{a} on the x-axis. A particle of mass m\text{m} and charge q0=−q2{\text{q}}_{0}=-\dfrac{\text{q}}{2} is placed at the origin. If charge q0{\text{q}}_{0} is given a small displacement (y \lt\lta)\text{(y \lt \lt a)} along the y-axis, the net force acting on the particle is proportional to :JEE Main/MCQ/Medium/Applications of SHM
  181. 181If a simple pendulum has significant amplitude (up to a factor of 1/e1 / e of original) only in the period between t=0st=0s to t=τst=\tau s, then τ\tau may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity, with 'bb' as the constant of proportionality, the average life time of the pendulum is (assuming damping is small) in seconds:JEE Main/MCQ/Medium/Applications of SHM
  182. 182Two springs, of force constants k1k_1 and k2k_2, are connected to a mass m\mathrm{m} as shown. The frequency of oscillation of the mass is f\mathrm{f}. If both k1k_1 and k2k_2 are made four times their original values, the frequency of oscillation becomes
    JEE Main/MCQ/Medium/Applications of SHM/With diagram
  183. 183The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillation bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation wouldJEE Main/MCQ/Medium/Applications of SHM
  184. 184If a spring has time period T, and is cut into n equal parts, then the time period of each part will beJEE Main/MCQ/Medium/Applications of SHM
  185. 185The amplitude and phase of a wave that is formed by the superposition of two harmonic travelling waves, y1(x,t)=4sin⁡(kx−ωt)\mathrm{y}_1(\mathrm{x}, \mathrm{t})=4 \sin (\mathrm{kx}-\omega \mathrm{t}) and y2(x,t)=2sin⁡(kx−ωt+2π3)\mathrm{y}_2(\mathrm{x}, \mathrm{t})=2 \sin \left(\mathrm{kx}-\omega \mathrm{t}+\frac{2 \pi}{3}\right), are ::
    (Take the angular frequency of initial waves same as     ω\omega)    JEE Main/MCQ/Medium/Superposition of S.H.M’s and Resonance
  186. 186Two simple harmonic waves having equal amplitudes of 8cm8cm and equal frequency of 10Hz10Hz are moving along the same direction. The resultant amplitude is also 8cm8cm. The phase difference between the individual waves is _____ degree.JEE Main/Numerical/Medium/Superposition of S.H.M's and Resonance
  187. 187The function of time representing a simple harmonic motion with a period of πω\dfrac{\pi }{\omega } is :JEE Main/MCQ/Medium/Superposition of S.H.M's and Resonance
  188. 188In forced oscillation of a particle the amplitude is maximum for a frequency ω1\omega_1 of the force, while the energy is maximum for a frequency ω2\omega_2 of the force, thenJEE Main/MCQ/Medium/Superposition of S.H.M's and Resonance
  189. 189Two light identical springs of spring constant kk are attached horizontally at the two ends of a uniform horizontal rod ABAB of length ll and mass m.m. The rod is pivoted at its center 'O' and can rotate freely in horizontal plane. The other ends of the two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is:

    JEE Main/MCQ/Medium/Angular oscillations/With diagram
  190. 190A rod of mass MM and length 2L2L is suspended at its middle by a wire. It exhibits torsional oscillations. If two masses, each of mass mm, are attached at a distance L/2L/2 from its centre on both sides, it reduces the oscillation frequency by 2020%. The value of ratio m/Mm/M is close toJEE Main/MCQ/Medium/Angular oscillations
  191. 191The angular frequency of the damped oscillator is given by, ω=(km−r24 m2)\omega=\sqrt{\left(\frac{\mathrm{k}}{\mathrm{m}}-\frac{\mathrm{r}^2}{4 \mathrm{~m}^2}\right)} where k\mathrm{k} is the spring constant, m\mathrm{m} is the mass of the oscillator and rr is the damping constant. If the ratio r2mk\frac{r^2}{\mathrm{mk}} is 8%8 \%, the change in time period compared to the undamped oscillator is approximately as follows:JEE Main/MCQ/Medium/Angular oscillations
  192. 192Bob of a simple pendulum of length ll is made of iron. The pendulum is oscillating over a horizontal coil carrying direct current. If the time period of the pendulum is T\mathrm{T} then :JEE Main/MCQ/Medium/Angular oscillations
  193. 193A ring is suspended from a point SS on its rim as shown in the figure. When displaced from equilibrium, it oscillates with time period of 1 second. The radius of the ring is (take g=π2g=\pi^2 )
    JEE Main/MCQ/Medium/Angular oscillations/With diagram
  194. 194A particle of mass mm is attached to a spring (of spring constant kk ) and has a natural angular frequency ω0\omega_0. An external force F(t)F(t) proportional to cos⁡ωt(ω≠ω0)\cos \omega t\left(\omega \neq \omega_0\right) is applied to the oscillator. The time displacement of the oscillator will be proportional toJEE Main/MCQ/Medium/Angular oscillations

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