At maximum displacement in a mass-spring system, which energy form is maximum?

• A. The total energy is zero at maximum displacement.
• B. The kinetic energy is maximum.
• C. The potential energy is maximum.
• D. The kinetic and potential energies are equal.

Answer: (C)

In this system, energy swaps between kinetic and potential as the mass oscillates, while the total energy stays constant. At the points of maximum displacement, the mass momentarily has zero velocity, so the kinetic energy is zero. The spring is stretched or compressed the most there, so the potential energy, which depends on the square of the displacement, is at its maximum. Therefore the energy form that is largest at maximum displacement is the spring’s potential energy (equal to the total energy, (1/2) k A^2). The kinetic energy is zero at that moment, so that option isn’t correct, and the total energy isn’t zero.