Question

The kinetic energy of a particle performing S.H.M. is `1/n` times its potential energy. If the amplitude of S.H.M. is 'A', then the displacement of the particle will be ______ 

Options

• nA

• `sqrt(((n + 1)A^2)/n)`

• `A/n`

• `sqrt((nA^2)/(n + 1))`

Answer 1

The kinetic energy of a particle performing S.H.M. is `1/n` times its potential energy. If the amplitude of S.H.M. is 'A', then the displacement of the particle will be `underline(sqrt((nA^2)/(n + 1)))`.

Explanation:

K.E. = `1/2momega^2(A^2 - x^2)` 

P.E. = `1/2momega^2x^2`

n KE = PE

`n(A^2 - x^2) = x^2`

`nA^2 - nx^2 = x^2`

`x^2(1 + n) = nA^2`

`x^2 = n/(1 + n)A^2`

x = `sqrt(n/(1 + n))A = sqrt((nA^2)/(n + 1))`