Oscillations

JEE Main level, single correct, medium

62 of 194

Question 62 of 194

A 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 :

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Answer: (C) (M+mM)1/2\left(\frac{\mathrm{M}+\mathrm{m}}{\mathrm{M}}\right)^{1 / 2}

Energy of simple harmonic oscillator is constant.
⇒12Mω2A12=12(m+M)ω2A22A12A22=M+mM∴A1A2=M+mM\begin{aligned} & \Rightarrow \frac{1}{2} M \omega^2 A_1^2=\frac{1}{2}(m+M) \omega^2 A_2^2 \\ & \frac{A_1^2}{A_2^2}=\frac{M+m}{M} \\ & \therefore \frac{A_1}{A_2}=\sqrt{\frac{M+m}{M}} \end{aligned}

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