A simple harmonic oscillator has an amplitude A. The potential energy is one-fourth of the total energy, when the displacement is,

Options

A. `A/sqrt2`
B. `A/2`
C. `A/4`
D. `A/2sqrt2`

Answer

b

Explanation

Total energy,`E=1/2momega^2A^2`
PE of simple harmonic oscillator ,`U=1/2momega^2y^2`
Given that,
`U=E/4`.
`1/2momega^2y2=1/4(1/2momega^2A^2)`
`implies y^A^2/4`
`y=sqrt(A^2)/(4)=A/2`