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

Answer

C

Explanation

Fsor SHM : P.E. `=(1)/(2)m omega^(2)x^(2)`
and `K.E.=(1)/(2)m omega^(2)(a^(2)-x^(2))`
For `x=(a)/(2)` then the ratio is
`(K.E.)/(P.E.)=(1//2m omega^(2)(a^(2)-a^(2)//4))/(1//2m omega^(2)(a^(2)//4))`
`(K.E.)/(P.E.)=(3a^(2)//4)/(a^(2)//4)=3:1`
So correct choice is ( c ).