L21, Phase Planes

Question 1

Objectives:

• To understand and interpret phase planes- a representation and visualisation of the state of a system component
• To apply phase plane diagrams to various movements

Answer 1

Summary:

• Phase plane diagrams show all states of the system
• Phase planes can represent mechanical energy
• Make not of the state of relevant components at key events

Question 2

What does the top of the axis in a swinging pendulum represent (the state of a moving object)?

Answer 2

One instant in time

Question 3

What does the bottom of the axis in a swinging pendulum represent (the state of a moving object)?

Answer 3

Pendulum’s position (relative to equilibrium position; right of equilibrium is +ve) vs time

Question 4

A pendulum with friction finished where?

Answer 4

Stationary at a point

Question 5

What does an angle in a phase plane represent?

Answer 5

Any point on the trajectory

Question 6

Why do we normalise both axis (centred phase angles)?

Answer 6

So the origin is in the centre of trajectory (enables phase angles of 0-360 degrees)