Question

Prove a freely swinging pendulum obeys law of conservation of energy.

Answer 1

When a pendulum is pulled to one side and released, its energy changes continually between gravitational potential energy (PE) and kinetic energy (KE).

• At either extreme position, the bob is momentarily at rest and is at its greatest height. Its PE is maximum and its KE is zero.
• As it swings towards the mean position, it loses height and gains speed. PE decreases while KE increases.
• At the mean position, the bob has its greatest speed, so its KE is maximum and its PE is minimum (taken as zero at this level).
• As it swings towards the other extreme, its speed decreases and height increases. KE changes back into PE. At that extreme, PE is maximum and KE is zero again.

Thus, throughout the swing, energy is transformed from PE to KE and back, while the total mechanical energy, PE + KE, remains constant. Therefore, a freely swinging pendulum obeys the law of conservation of energy, assuming air resistance and friction are negligible.