# The
Pendulum** - energy transitions**

Consider a **point pendulum
bob** connected to a **massless rope or rod **that is held at an angle
q from the horizontal. If you release the mass, then the system
will swing to a position at an angle q from the horizontal on the other side and back again to its starting position. This is **one full period **of the swing.

It can be determined that:

where

T is the period,
or time for one complete swing,

l is the length
- the distance from the point of suspension to the center of gravity
of the bob. Care has to be taken that the point of suspension is a
point - this can be achieved by clamping the string frimly between
two pieces of card.

g is the acceleration
of gravity.

**Energy** **Transitions**

The **mechanical energy
of the ideal pendulum is a conserved**.

The **gravitational potential energy** of the pendulum,
mgΔh, increases with the height of the bob, therefore the potential energy
is minimized at the equilibrium point and is maximized at the extreme
positions.

Conversely, the **kinetic energy **and **velocity of the pendulum** are maximized at the equilibrium point and minimized at the extremes..