Question:
Find the displacement of a simple harmonic oscillator at which its PE is half of the maximum energy of the oscillator.
Solution:
The mean position of the oscillator at x with PE = 1/2 kx2
PE = -m2x2
When PE is maximum, KE = 0 at x = A
E = 1/2 mω2A2
PE = 1/2 total energy
x2 = 1/2 A2
x = ± A/√2