A mass M, attached to a horizontal spring, executes S.H.M. with amplitude A1. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A2. The ratio of is :

Engineering

Physics

Basics of Simple Harmonic Motion

Question

A mass M, attached to a horizontal spring, executes S.H.M. with amplitude A₁. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A₂. The ratio of $(\frac{A_{1}}{A_{2}})$ is :

$\frac{M + m}{M}$

$\frac{M}{M + m}$

${(\frac{M}{M + m})}^{1 / 2}$

${(\frac{M + m}{M})}^{1 / 2}$

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C.O.L.M. MV_max = (m + M)V_new , V_max = A₁w₁

_{${V_{new}} = \frac{{M{V_{\max }}}}{{(m + M)}}$}

Now, V_new = A₂.w₂

_{$\frac{{M.{A_1}}}{{(m + M)}}\sqrt {\frac{K}{M}} = {A_2}\sqrt {\frac{K}{{(m + M)}}} $}

_{${A_2} = {A_1}\sqrt {\frac{M}{{(m + M)}}} $ $\frac{{{A_1}}}{{{A_2}}} = {\left( {\frac{{m + M}}{M}} \right)^{1/2}}$}