Which term describes vibration about an equilibrium position with a restoring force proportional to displacement?

• A. Oscillation
• B. Simple Harmonic Motion
• C. Vibration
• D. Circular motion

Answer: (B)

When a system vibrates about an equilibrium position and the restoring force grows in direct proportion to how far it is displaced, the motion is simple harmonic motion. This means the acceleration is always directed toward the equilibrium and proportional to the displacement, so the motion traces a smooth, sinusoidal path. In mathematical terms, F = -k x leads to a''(t) = -(k/m) a(t), whose solutions are sine or cosine waves with frequency ω = sqrt(k/m). This describes the classic mass-on-a-spring or a pendulum for small angles, where the same proportional relationship holds.

This is what makes the motion uniquely simple and predictable: the same shape repeats over time with a constant period (in the ideal, undamped case). Other terms describe different kinds of motion—some back-and-forth movements without a restoring force that scales with displacement, or motion along a circular path that isn’t centered on a single equilibrium point.