Oscillations

JEE Main level, numerical answer, medium

36 of 194

Question 36 of 194

Two 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.

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Answer: 2

A1=5{A}_{1}=5
x2=52[sin⁡2πt+cos⁡2πt]{x}_{2}=5\sqrt{2}[\sin 2\pi t+\cos 2\pi t]
x2=10[sin⁡(2πT+π4)]{x}_{2}=10\left[\sin \left(2\pi T+\dfrac{\pi }{4}\right)\right]
A2=10{A}_{2}=10
A2=2A1{A}_{2}=2{A}_{1}

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