An experimenter sets up a horizontal mass–spring oscillator on a near-frictionless air track. The cart of mass 0.60kg oscillates with amplitude 0.25m about the equilibrium position x=0. At a certain instant the cart is observed to be at x=0.10m moving toward the equilibrium position.
(a) Calculate the numerical value of the fraction of the total mechanical energy that is kinetic at the observed instant.
(b) Determine the magnitude of the cart’s speed at that same instant if the period of oscillation is 0.80s.
(c) Interpret physically why the fraction obtained in part (a) depends only on the ratio x/A and not on the mass or spring constant.