A low-friction cart of mass 0.50 kg is attached to a horizontal ideal spring that is fixed to a wall. The cart is pulled 0.20 m to the right of the spring–cart system’s equilibrium position and held at rest before being released at time t=0.
(a) Describe the direction of the cart’s acceleration during the first half-cycle of its motion. In your answer, refer explicitly to the cart’s location relative to the equilibrium position.
(b) Without using any specific equations, explain why the magnitude of the cart’s acceleration is greatest at the endpoints of its motion and zero when the cart passes through the equilibrium position.
(c) Suppose the spring constant were doubled while all other quantities remained the same. Describe qualitatively how, if at all, the acceleration–versus-time graph for the cart would change during the first half-cycle.