1. The problem statement, all variables and given/known data This is from Advanced Physics by Adams and Allday. Spread 3.34, Q 3. A friction-free trolley of mass 2 kg is tethered to rigid supports at each end by two identical springs of spring constant 20 N/m each. The springs obey Hooke's law and remain in tension as the trolley is displaced 2 cm to one side and released. What is the effective spring constant of the system tethering the trolley? 2. Relevant equations [itex]F = - k x[/itex] Where F is restoring force k is spring (stiffness) constant x is displacement from equilibrium position 3. The attempt at a solution In the equilibrium position let each spring be stretched by x generating a restoring force F(each x and F are identical by symmetry). Move the trolley [itex]\delta x[/itex] to the right ([itex]\delta x < x[/itex]). The extension of the left spring is now [itex]x + \delta x[/itex] and the right spring [itex]x - \delta x[/itex]. The restoring force from the left spring is now [itex]F_L = - k ( x + \delta x)[/itex] The restoring force from the right spring is now [itex]F_R = - k ( x - \delta x)[/itex] The net force (on the trolley), acting to restore the previous equilibrium position is [itex]F_L - F_R[/itex] [itex]= - k ( x + \delta x) - (- k ( x - \delta x)[/)[/itex] [itex]= - 2 k \delta x[/itex] Thus the spring constant of the system is twice the spring constant of the individual springs, that is 40 N/m. The answer given in the textbook is 10 N/m. What is the right answer?