Where does a pendulum keep time?

Lift the bob and hold it still. It has no speed yet, but it sits above its lowest point. Release it, and that height begins turning into motion. Follow a full swing to separate energy from timing.

The string constrains the bob to a circular arc. Gravity points downward; its tangential component accelerates the bob toward the bottom. The string mainly redirects motion and does no work in this ideal model.

Watch the crossing. At the lowest point, the potential-energy bar is short and the kinetic-energy bar is long. The bob does not stop there: its accumulated speed carries it onward toward the other side.

On the way up, speed turns back into height. At the far end the bob pauses, but its energy has not vanished; most is potential again. Gravity then brings it back through the same exchange.

What counts as one oscillation? A complete period returns to the same position with the same direction of motion. Left endpoint to right endpoint is only half a period. The angle trace records that repeating pattern.

Use a longer string and release from the same angle. The motion takes longer. For small swings, period grows with the square root of length, so doubling the length does not double the period.

Make the bob heavier while keeping the length and release angle fixed. Its energy rises, but the rhythm stays the same. Gravitational force and inertia both scale with mass, so mass cancels from the motion equation.

Now move the experiment to the Moon. Keep length and mass fixed, and reduce gravity. The restoring effect weakens, so each swing takes longer. A pendulum clock calibrated on Earth would not keep the same time there.

Back on Earth, release from a much larger angle. The familiar period formula assumes a small swing. This simulation uses the nonlinear equation, so large swings take longer; the small-angle readout is only an approximation.

Add damping. Each return reaches a little less height, and the total of kinetic and potential energy falls. Energy is not destroyed; resistance and friction transfer it into the surroundings, mostly as heat.

A clock cannot run forever on one release. Real pendulum clocks draw energy from a weight or spring to replace losses. There is no escapement in this experiment, so damping eventually brings the bob to rest.

Separate the three questions. Length and gravity mainly set the rhythm, damping controls the fading amplitude, and mass sets the energy scale. With those relationships in mind, every change in the experiment has a reason.