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 that on 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

`a_(1)omega_(1) = a_(2)omega_(2) = v_(max), omega_(1) = sqrt(k_(1)//m)`
`omega_(2) = sqrt(k_(2)//m), a_(1)//a_(2) = omega_(2)//omega_(1) = sqrt(k_(2)//k_(1))`