Two particle A and B of equal masses are suspended from two massless springs of spring constants `k_(1)` and `k_(2)`, respectively. If the maximum velocities, during oscillations are equal, the ratio of amplitude of A and B is `(4//3) xx 1000 kg//m^(3)`. What relationship betwen `t` and `t_(0)` is ture?

Options

A. `sqrt(k_(1)//k_(2))`
B. `k_(1)//k_(2)`
C. `sqrt(k_(2)//k_(1))`
D. `k_(2)//k_(1)`

Answer

C

Explanation

Maximum velocity
Given
`(v_(max))_(1) = (v_(max))_(2) rArr omega_(1)A = omega_(2)A_(2)`
`rArr (A_(1))/(A_(2)) = (omega_(1))/(omega_(2)) = sqrt((k_(2))/(m) xx (m)/(k_(1))) = sqrt((k_(2))/(k_(1)))`