The one value of total energy that the pendulum has throughout its oscillations is all potential energy at the endpoints of the oscillations, all kinetic energy at the midpoint, and a mix of potential and kinetic energy at locations in between.

Once the weighted end of the pendulum is released, it will become active as gravity pulls it downward. Potential energy is converted to kinetic energy, which is the energy exerted by a moving object.

The potential energy of the pendulum is 0 when the pendulum is at its equilibrium position. Therefore, at this point, the mechanical energy E is equal to the kinetic energy KE (all the energy at the equilibrium position is kinetic).

At every point in the motion of the pendulum the total mechanical energy is conserved. The sum of the gravitational potential energy and the kinetic energy, at each point of the motion, is a constant, which is the total mechanical energy.

In a simple pendulum with no friction, mechanical energy is conserved. Total mechanical energy is a combination of kinetic energy and gravitational potential energy. As the pendulum swings back and forth, there is a constant exchange between kinetic energy and gravitational potential energy.

A pendulum is a simple example of energy transfer. When it is allowed to swing, that energy is gradually converted to energy of motion – kinetic energy. When the pendulum is at position B, all of its potential energy has been converted to kinetic energy and it is moving at its maximum speed.

While not all of the energy from the bullet is transformed into kinetic energy for the pendulum (some is used as heat and deformation energy) , the momentum of the system is conserved. In the case of a pendulum total mechanical energy is conserved.

Momentum of the pendulum is not conserved, because it is constantly changing during the flight of the pendulum. As you noted, gravity is acting on it.

The ballistic pendulum is a device in which a projectile such as a bullet is fired into a suspended heavy wooden stationary block. Some kinetic energy gets transformed into heat and sound, and some is used to deform the block. However, momentum is conserved.

If momentum is conserved in the collision of the ball and pendulum, the speed V of the ball and pendulum just after the collision can be calculated from the masses of ball and pendulum and the speed of the ball just before the collision. Pi = Pf is the statement of momentum conservation.

a law, discovered by Galileo in 1602, that describes the regular, swinging motion of a pendulum by the action of gravity and acquired momentum. the theory holding that trends in culture, politics, etc., tend to swing back and forth between opposite extremes.

The pendulum stops eventually because of air resistance. The pendulum loses energy because of friction. Only in a theoretical situation when there is no friction the pendulum will oscillate forever.

To slow the Grandfather Clock down, move the pendulum disk down by turning the adjustment nut to the left. To speed the Grandfather Clock up, move the pendulum disk up by turning the adjustment nut to the right.