Which term specifically refers to back-and-forth motion with a restoring force proportional to displacement?

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Multiple Choice

Which term specifically refers to back-and-forth motion with a restoring force proportional to displacement?

Explanation:
Simple harmonic motion is back-and-forth motion in which the restoring force is proportional to the displacement from equilibrium and directed toward that equilibrium. This means F = -k x, so for a mass on a spring with negligible damping the equation of motion is m d^2x/dt^2 = -k x. The solutions are sinusoidal in time, x(t) = A cos(ω t + φ), with angular frequency ω = sqrt(k/m) and period T = 2π sqrt(m/k). The motion repeats with a constant amplitude when damping is small, reflecting the precise linear restoring-force relationship. Tremor is irregular, and frequency is a rate descriptor, not the specific restoring-force behavior.

Simple harmonic motion is back-and-forth motion in which the restoring force is proportional to the displacement from equilibrium and directed toward that equilibrium. This means F = -k x, so for a mass on a spring with negligible damping the equation of motion is m d^2x/dt^2 = -k x. The solutions are sinusoidal in time, x(t) = A cos(ω t + φ), with angular frequency ω = sqrt(k/m) and period T = 2π sqrt(m/k). The motion repeats with a constant amplitude when damping is small, reflecting the precise linear restoring-force relationship. Tremor is irregular, and frequency is a rate descriptor, not the specific restoring-force behavior.

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