A light horizontal spring is fixed to a wall on its left end. A small cart of mass m is attached to the free end of the spring and can glide without friction along a straight track. The track’s origin x=0 is defined at the spring’s equilibrium length. Three instants during an experiment are noted:
• Instant 1: the cart is at x=+0.050m (to the right of equilibrium).
• Instant 2: the cart is at x=0.
• Instant 3: the cart is at x=−0.050m (to the left of equilibrium).
Answer the following questions about the restoring force exerted on the cart by the spring.
(a) For each of the three instants, state the direction (left or right) of the restoring force acting on the cart.
(b) Describe quantitatively how the magnitude of the restoring force depends on the cart’s displacement x from equilibrium. Include the role of proportionality and any physical constant that characterizes the spring.
(c) Without performing any numerical calculation, describe the overall shape, slope, and intercept of a graph of restoring force Fspring (vertical axis) versus displacement x (horizontal axis). Explain how the graph reflects both the magnitude–displacement relationship and the force’s direction.