Question

At what distance from the mean position is the kinetic energy of a particle performing S.H.M. of amplitude 10 cm, three times its potential energy?

Answer 1

Given:

Amplitude A = 10 cm = 0.10 m

KE = 3 × PE

Total Energy: `E = 1/2 mω^2A^2`

`KE = 1/2 mω^2 (A^2 - x^2)`

`PE = 1/2 mω^2x^2`

KE = 3 × PE

`1/2 mω^2(A^2-x^2) = 3xx1/2mω^2x^2`

A² − x² = 3x²

A² = 4x² 

`x^2 = A^2/4 => x=A/2`

`x=10/2`

= 5 cm