Find the displacement of a simple harmonic oscillator at which its PE is half of the maximum energy of the oscillator.

Answer:

we know that the mean position of the oscillator at x with PE is

= 1/2 kx²

Therefore, PE = -m²x²

When PE is maximum, KE = 0 at x = A

We get, E = 1/2 mω²A²

PE = 1/2 total energy

x² = 1/2 A²

x = ± A/√2