# Pendulum Animation

Play with a pendulum.

This is a good example of a mathematical model. Each unit of time is calculated using the data from from the previous unit of time, and the motion you see is the result.

For example the Period is timed (not an in-built formula) so it takes a short while to find a value (and may vary a little).

KE means Kinetic Energy (the energy of motion), and PE means Potential Energy (in this case the energy available by falling, so it is zero when at the lowest point).

What are KE and PE?

• Potential Energy (PE) is stored energy due to position or state
• PE due to gravity = m g h

• Kinetic Energy (KE) is energy of motion
• KE = ½ m v2

The KE and PE are constantly calculated and you can see that their total stays the same (apart from some slight changes due to errors in calculation).

There is no friction or drag in this model, so the pendulum keeps going. In the real world it would slow down.

Things to try:

• Change the length. Does it change the motion?
• Change the mass. Does it change the motion?
• Change the gravity. Does it change the motion?
• What happens at low or zero gravity?
• Suddenly increase the mass when that ball is at its highestor lowest. What happens?