A mass M attached to a horizontal spring exec | vedclass

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(C) At the mean position,the velocity of the mass $M$ is maximum,given by $v_1 = \omega_1 A_1 = \sqrt{\frac{k}{M}} A_1$.When mass $m$ is added at the

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

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(C) At the mean position,the velocity of the mass $M$ is maximum,given by $v_1 = \omega_1 A_1 = \sqrt{\frac{k}{M}} A_1$.When mass $m$ is added at the mean position,the momentum is conserved because the spring force is zero at the mean position.Let $v_2$ be the velocity of the combined mass $(M+m)$ immediately after adding $m$.By conservation of linear momentum: $M v_1 = (M+m) v_2$.Substituting the expressions for velocity: $M \left( \sqrt{\frac{k}{M}} A_1 \right) = (M+m) \left( \sqrt{\frac{k}{M+m}} A_2 \right)$.Simplifying the equation: $\sqrt{Mk} A_1 = \sqrt{(M+m)k} A_2$.Therefore,$\frac{A_1}{A_2} = \sqrt{\frac{M+m}{M}}$.

$A$ mass $M$ attached to a horizontal spring executes simple harmonic motion with amplitude $A_1$. When mass $M$ passes the mean position,a smaller mass $m$ is attached to it,and both of them together execute simple harmonic motion with amplitude $A_2$. Then the value of $\frac{A_1}{A_2}$ is

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