Q: Two bodies M and N of equal masses are suspended from two separate massless spring constant k_{1} and k_{2} respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the one amplitude of vibration of M to that of N is

(a) $\large \frac{k_1}{k_2}$

(b) $\large \sqrt{\frac{k_2}{k_1}}$

(c) $\large \frac{k_2}{k_1}$

(d) $\large \sqrt{\frac{k_1}{k_2}}$

Ans: (b)

Sol: According to question ,

$\large (v_M)_{max} = (v_N)_{max} $

$\large \omega_M A_M = \omega_N A_N $

$\large \frac{A_M}{A_N} = \frac{\omega_N}{\omega_M}$

Since , $\large \omega = \sqrt{\frac{k}{m}} $

$\large \frac{A_M}{A_N} = \sqrt{\frac{k_2}{k_1}}$