Two bodies M and N of equal masses are suspended from two separate massless springs of spring constants `k_1` and `k_2` respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of M to the of N is.

Options

A. `(k_1)/(k_2)`
B. `sqrt((k_1)/(k_2))`
C. `(k_2)/(k_1)`
D. `sqrt((k_2)/(k_1))`

Answer

D

Explanation

Both the bodies oscillate in simple harmonic motion, for the maximum velocities will be
Given that `v_1 = v_2 rArr a_1 omega_1 = a_2 omega_2`
:. `a_1 xx (2 pi)/(T_1) = a_2 xx (2 pi)/(T_2)`
`rArr (a_1)/(a_2) = (T_1)/(T_2) = (2 pi sqrt(m)/(k_1))/(2 pi sqrt(m)/(k_2)) = sqrt(k_2/(k_1))`.