In a mass-spring system undergoing SHM, where is the potential energy maximum?

• A. At the resting point
• B. At intermediate positions
• C. At the maximum displacement
• D. At all points equally

Answer: (C)

The amount of potential energy in a mass-spring system is (1/2) k x^2, where x is the displacement from equilibrium. This energy grows with the size of the stretch or compression, so it is largest when the mass is at the maximum displacement (the amplitude). At that turning point, the velocity is zero, so all the energy is stored as potential energy. At the equilibrium position, x = 0 and the potential energy is zero; at intermediate positions, the potential energy is between zero and its maximum. Thus the maximum potential energy occurs at the maximum displacement.