At the equilibrium position x = 0, the kinetic energy is:

At the equilibrium position x = 0, the kinetic energy is:

• A. Maximum
• B. Zero
• C. Equal to total energy
• D. Not defined

Answer: (A)

In simple harmonic motion, speed is largest as the mass passes through the equilibrium position. Kinetic energy depends on speed through K = (1/2) m v^2, so when v is at its maximum, the kinetic energy is at its maximum as well. The restoring force is zero there, but the mass is moving fastest, so all that energy is in motion rather than in the spring’s potential energy. Because the total energy stays the same, the maximum kinetic energy at x = 0 reflects the point where potential energy is at its minimum. This is why the kinetic energy is maximum at the equilibrium position.

In simple harmonic motion, speed is largest as the mass passes through the equilibrium position. Kinetic energy depends on speed through K = (1/2) m v^2, so when v is at its maximum, the kinetic energy is at its maximum as well. The restoring force is zero there, but the mass is moving fastest, so all that energy is in motion rather than in the spring’s potential energy. Because the total energy stays the same, the maximum kinetic energy at x = 0 reflects the point where potential energy is at its minimum. This is why the kinetic energy is maximum at the equilibrium position.