Question

when he displacement of a mass on a spring is half the amplitude of the oscillation, what fraction of the mass's energy is kinetic energy?

Answer 1

PE = 1/2 K x^2 potential energy

when x = A

PEt = 1/2 k A^2 total potential energy

If x = A / 2

PE 1/2= 1/2 k A^2 / 4

PE1/2 / PEt = 1/4

Thus the PE at 1/2 the displacement is 1/4 the total

Since PE + KE = constant

3/4 the mass's energy will be KE at 1/2 the amplitude