In simple harmonic motion, how do the frequency and period depend on amplitude?

• A. Both depend on amplitude
• B. Frequency depends on amplitude, but period does not
• C. Frequency and period are independent of amplitude
• D. Amplitude determines the period

Answer: (C)

In simple harmonic motion, the timing of a cycle is set by the system’s inertia and restoring strength, not by how far you release it. The equation of motion for a mass on a spring is m d^2x/dt^2 = -k x. This leads to an angular frequency ω = sqrt(k/m), so the frequency is f = ω/(2π) and the period is T = 2π/ω. Since ω depends only on k and m, neither f nor T changes with the amplitude A (the maximum displacement).

The amplitude only determines the energy of the motion, E = (1/2) k A^2, not the rate at which the oscillator goes back and forth. In the ideal small-angle pendulum case, the period is also independent of amplitude, reinforcing that the oscillation’s timing isn't set by how far you swing it, but by the system’s physical parameters. So, both frequency and period do not depend on amplitude in ideal simple harmonic motion.