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

Data: A = 10 cm, KE = 3PE

KE = `1/2 k(A^2 - x^2)` and PE = `1/2 kx^2`

Given, KE = 3PE

∴ `1/2 k(A^2 - x^2) = 3(1/2 kx^2)`

∴ A² − x² = 3x²

∴ 4x² = A²

∴ The required displacement is

x = `±A/2`

= `± (10  cm)/2`

= ± 5 cm