A pendulum clock keeps accurate time because its pendulum swings in simple harmonic motion. Explain what is meant by simple harmonic motion and describe how the amplitude and time period of the pendulum's swing change as the clock continues to run over several hours without any external energy input.

Simple harmonic motion (SHM) is a type of oscillatory motion in which the restoring force (or acceleration) acting on the system is directly proportional to the displacement from the equilibrium position and directed towards that equilibrium. In a pendulum clock the restoring torque is produced by gravity and is proportional to the angular displacement.

Because the restoring force is proportional to displacement, the time period of the oscillation is independent of the amplitude. Thus, as the pendulum loses energy to air resistance and friction at the pivot, its amplitude gradually decreases, but the time period remains essentially unchanged. The constant time period means each swing still represents the same interval of time, allowing the clock to keep accurate time even though the swings become smaller.

Examiner_tips:
- Define SHM with the two key properties: restoring force proportional to displacement and directed towards equilibrium.
- State that the time period is independent of amplitude.
- Explain that energy loss reduces amplitude but not period.
- Link the constant period to accurate timekeeping.

common_mistakes:
- Confusing the restoring force with the driving force.
- Claiming the period changes with amplitude.
- Forgetting to mention energy loss mechanisms (air resistance, friction).