Oscillations

JEE Main level, single correct, medium

169 of 194

Question 169 of 194

Two 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 :

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Answer: (A) πmk\pi \sqrt{\dfrac{m}{k}}

For parallel combination keq=k1+k2{k}_{eq}={k}_{1}+{k}_{2}
keq=4k{k}_{eq}=4k
T=2πmkeq⇒T=2πm4k⇒T=πmkT=2\pi \sqrt{\dfrac{m}{{k}_{eq}}} \Rightarrow T=2\pi \sqrt{\dfrac{m}{4k}} \Rightarrow T=\pi \sqrt{\dfrac{m}{k}}

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