In the pulley system shown in Fig. 2.1, the input is the applied force F, and the output is displacement, x. Assume the pulley masses are negligible and derive the equations of motion using Newton's 2nd law. (Hint: You need to account for the pulleys in the deflection of the spring.) - NOTE: DO NOT USE WORK-ENERGY METHODS IN SOLUTION. YOU WILL NOT GET CREDIT USING THE SOLUTION COVENIENTLY FOUND ONLINE