Illustrate the law of conservation of energy by discussing the energy changes which occur when we draw a pendulum bob to one side and allow it to oscillate. Why does the bob eventually come to rest? What happens to its energy eventually? Is it a violation of the law of conservation of energy?

The law of conservation of energy states that energy can be neither created nor destroyed. It can only be converted from one form to another.

Consider the case of an oscillating pendulum.

When a pendulum moves from its mean position P to either of its extreme positions A or B, it rises through a height h above the mean level P. At this point, the kinetic energy of the bob changes completely into potential energy. The kinetic energy becomes zero, and the bob possesses only potential energy. As it moves towards point P, its potential energy decreases progressively. Accordingly, the kinetic energy increases. As the bob reaches point P, its potential energy becomes zero and the bob possesses only kinetic energy. This process is repeated as long as the pendulum oscillates.

The bob does not oscillate forever. It comes to rest because air resistance resists its motion. The pendulum loses its kinetic energy to overcome this friction and stops after some time.

The law of conservation of energy is not violated because the energy lost by the pendulum to overcome friction is gained by its surroundings. Hence, the total energy of the pendulum and the surrounding system remain conserved.

In physics, the law of conservation of energy states that the total power of an isolated system remains constant and that energy can neither be created nor destroyed; instead, it can transform from one form to another.
When a pendulum moves from its central position to either of its extremes, it rises through a height above the mean level. At this point, the K.E. of the bob changes into P.E.As it moves back to the central position, its P.E. decreases progressively, and K.E. increases. As the bow reaches the central location, it has only K.E.This Process is repeated as long as the bob oscillates.
The bob eventually comes to rest because the air resistance resists its motion, and the pendulum loses its K.E. to overcome this friction and stops after some time.
The law of conservation of energy isn't violated as the energy lost by the pendulum is gained by its surroundings.