# 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 the previous unit of time, and the motion you see is the result.

For example the period is timed from top to bottom (not an in-built formula) so it can take a short while to find a value, and can vary a little due to calculation accuracy.

What are PE and KE?
• 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 slight changes due to rounding).

Why is the total constant? Because one type of energy is converted to the other and back again.

It is really cool how this works!

Notice how PE is highest at the top of the swing and zero at the bottom.

And KE is highest when the pendulum swings the fastest (at the bottom of the arc).

Use pause to look at the values.

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 highest or lowest. What happens?
• Can you increase its speed by changing the length in rhythm with the swing?