A particle oscillation is given by `(f_(0)) = kpl^(2)` with for constant `k` and an amplitude A The maximum velocity during the oscillation a preperitiaonal to :

Options

A. `A`
B. `A^(2)`
C. `A^(3//2)`
D. none of these

Answer

C

Explanation

Let at any time displacement is `y` and velocity is `s` since total energy can be the maximum `PE` we get
`(1)/(2) mv^(2) + ky^(3) = kA^(3) rArr = sqrt((2k(A^(2)- y^(3)))/(m))`
Velocity maximum is therefore `(at y = 0)`
`v_(max) = sqrt((2kA^(2))/(m)) rArr v_(max) prop A^(1//2)`