Question

At what distance from the mean position is the kinetic energy of a particle performing S.H.M. of amplitude 8 cm, three times its potential energy?

Answer 1

Given : A=8 cm, KE = 3PE

KE = \(\frac{1}{2}\)k(A² —x²) and PE = \(\frac{1}{2}\)kx²

Given, KE = 3PE.

∴ \(\frac{1}{2}\) k(A² —x²) = 3( \(\frac{1}{2}\) kx²)

∴ A² —x² = 3x² ,  ∴ 4x² = A²

the required displacement is

x = ± A/2 = ±8/2 = ±4 cm