The ratio of kinetic energy to the potential energy of a particle executing SHM at a distance equal to half its amplitude, the distance being measured from its equilibrium position is

Options

A. `8: 1`
B. `2: 1`
C. `4: 1`
D. `3: 1`

Answer

D

Explanation

Potential energy `U= (1)/(2) kx^(2)= (1)/(2)k (A^(2))/(4)` Where `x = (A)/(2)`
Kinetic energy `K = (1)/(2) kA^(2)- (1)/(2) k(A^(2))/(4)= (3)/(8) kA^(2)`
Hence `(K)/(U)= (3//8)/(1//8)= 3: 1`