Question

An object is suspended from a spring and vibrates with simple harmonic motion. At an instant when the displacement of the object is equal to one-half the amplitude, what fraction of the total energy of the system is kinetic and what fraction is potential?

Answer 1

Potential energy of a vibrating spring is proportional to the square of the displacement (P.E = kx^2/2, where k is the spriong constant). At maximum displacement, ALL of the energy is potential energy, because motion temporaily stops and KE is zero. At 1/2 maximum displacement, the P.E. is 1/4 of that total energy. That means that 3/4 must be kinetic energyn there.