show that the total energy is conserved in the oscillation of pendulum?

A oscillating pendulum is a body whose energy can either be potential or kinetic or a mixture of potential and kinetic,but its total energy at any instant of time remains the same.

Initially the simple pendulum is at rest with its bob in the center position lets say A.When the bob is pulled to one side to position B and then released the bob starts swinging between extreme positions B and C.

At B-It has only potential energy no kinetic energy.

As the bob starts moving down from B to A,its potential energy goes on decreasing but its kinetic energy goes on increasing.

When it reaches A,it has only kinetic energy, no potential energy.

As the bob goes from A towards C its kinetic energy goes on decreasing but the potential energy goes on increasing.

On reaching C the bob stops for a very small instant of time.So here is only potential energy but no kinetic energy.

Thus we see from the above that the total energy at any instant remains conserved (it is transformed from one form to another.)

Hope this helps.