In a mass-spring system, which statement correctly describes the distribution of kinetic and potential energy during the motion?

• A. KE is greatest at extremes; PE greatest at resting point.
• B. KE and PE are both greatest at equilibrium.
• C. KE is greatest at resting point; PE greatest at extremes.
• D. KE is zero at the resting point; PE is zero at extremes.

Answer: (C)

In a mass-spring system undergoing simple harmonic motion, energy constantly shifts between kinetic energy, which grows with speed, and spring potential energy, which grows with displacement from equilibrium. When the mass passes through the equilibrium position, it moves fastest, so the kinetic energy is at its maximum and the spring is neither stretched nor compressed, giving the minimum (often zero) potential energy. As the mass moves toward an extreme, its speed drops to zero at the turning point, so the kinetic energy drops to zero and the spring is stretched or compressed the most, giving the maximum potential energy. Because total mechanical energy stays the same (ignoring damping), the sum KE + PE is constant.

So the correct description is that kinetic energy is greatest at the resting (equilibrium) point, and potential energy is greatest at the extremes. Choices that place the energy maxima at opposite points would contradict the motion and energy conservation.