Two bodies A and B of equal mass are suspended from two separate massless springs of spring constant `k_1 and k_2` respectively. If the bodies iscillte vertically such that their maxixum velocities are equal, the ratio of the amplitude of A to that of B is

Explanation

Let the amplitude of mass A and mass B are `a_(1) and a_(2)` respectively. Since their maximum velocities are equal, hence `v = a_(1) omega_(1) = a_(2) omega_(2)`
`rArr" "(a_(1))/(a_(2))=(omega_(2))/(omega_(1))rArr (a_(1))/(a_(2)) = (sqrt(k_(2)//m))/(sqrt(k_(1)//m)) = (a_(1))/(a_(2)) = sqrt((k_(2))/(k_(1)))`