For a particle executing `SHM`, the kinetic energy `(K)` is given by `K = K_(0)cos^(2) omegat`. The equation for its displacement is

Options

A. `k_(0)/(momega^(2))^(1//2) sin omega t`
B. `((2k_(0))/(momega^(2)))^(1//2) sin omega t`
C. `((2omega^(2))/(mk_(0)))^(1//2) sin omega t`
D. `((2k_(0))/(momega))^(1//2) sin omega t`

Answer

B

Explanation

If m is the mass, r is the amplitude of oscillation, then maximum kinetic energy,
`k_(0) = 1/2 momega^(2)r^(2)` or `r = ((2k_(0))/(momega^(2)))^(1//2)`

The displacement equation can be-
`y = r sin omegat = ((2k_(0))/(momega^(2)))^(1//2) sin omega t`