A 1.2kg cart is placed on a nearly frictionless track between two horizontal ideal springs that are fixed to opposite walls. The spring on the left has spring constant k1=40N/m, and the spring on the right has spring constant k2=60N/m. The equilibrium position of the cart is halfway between the two unstretched springs. The cart is pulled 0.10m to the right of equilibrium and released from rest at t=0.
(a) Write an expression for the net horizontal force acting on the cart when it is displaced a distance x to the right of equilibrium (x>0).
(b) Determine the cart’s instantaneous acceleration immediately after it is released.
(c) After some time the cart moves leftward past the equilibrium position and is observed at x=−0.05m. Calculate the magnitude and direction of its acceleration at that instant.
(d) Discuss qualitatively how the difference in the two spring constants affects the maximum displacement the cart attains on the left side compared with the right side during its subsequent motion.