Explain how potential energy, kinetic energy, and total mechanical energy change form in a swinging pendulum, and how the speed changes as a pendulum swings back and forth without friction. include the pendulum at its initial position, when it is moving downward, when it is at its lowest point, and when it is on the rise again.

Potential energy is associated with height ie PE = mgh
Kinetic energy is associated with velocity ie KE = 1/2 m v^2
Total energy is sum of potential and kinetic energies ie TE = PE + KE

Now as a pendulum swings ,It has certain energy associated with it.This energy content, that is the total mechanical energy, is constant as long as the pendulum swings in no friction condition.This TE is the sum of PE and KE .

Now considering the lowest point of pendulum bob as reference

**At the lowest point PE is zero because,h is zero.So the only energy present is KE and it is maximum because,velocity is maximum at lowest point.Again as the total energy is constant, so
TE = KE (PE is zero)

**At the highest point velocity is zero ,so KE is zero.And at the highest point h is maximum,so only PE is present and it is maximum,So TE
TE = PE (KE is zero)

**At a point between the highest and lowest,both KE and PE are present and the TE is given by
TE = KE + PE