Question

A pendulum is oscillating on either side of its rest position. Explain the energy changes that takes place in the oscillating pendulum. How does the mechanical energy remains constant in it? Draw the necessary diagram.

Answer 1

Energy changes: at B

K.E. = 0     ...[∵ at highest point velocity = 0]

P.E. = mgh   ...[∵ the bob is at height h]

∴ K.E. + P.E. = 0 + mgh = mgh    ...(i)

At A, the bob's height continues to drop as it travels from B to A, and its h at A is zero, but its velocity continues to rise. 

∴ At A P.E. = 0

K.E = mgh

∴ P.E. + K.E. = 0 + mgh = mgh     ...(ii)

At C, the bob is still travelling forward from B to C.

Its height increases to h at C, but its velocity continues to decrease until it reaches its maximum point, C, when velocity = 0.

∴ At C

K.E. = 0

P.E. = mgh

∴ K.E. + P.E. = 0 + mgh = mgh     ...(iii)

As a result, we discover that the total of K.E. and potential energy, or mechanical energy, stays constant, which is consistent with the energy conservation equation.