The pendulum bob is dropped from point a and swings to point c. the pendulum bob swings back and forth but eventually it stops. why?

A pendulum will continue to swing as long as there's no loss of energy and air resistance.

One of the reasons a pendulum stops is due to air resistance. When the value of friction in between the string and the pulley is 0, the swinging pendulum stops; the reason being that each swing the pendulum comes into contact with air molecules and the initial force (push) or positive force (gravity) is dissipated.

Another reason is loss of energy.

When a pendulum stops oscillating, it could be as a result of its inability energy loss which could be converted into heat.

The cause of this could be when the friction which exists with the point around which the pendulum rotates makes the system to lose kinetic energy; this will definitely stop.