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Five Circuits, Seven Spins

Age 16 to 18 Challenge Level:

A circular plate has radius one unit. It rolls around inside a rectangular tray, always touching the edge, and returns to its starting position after five circuits of the tray. During this time it rotates about its own centre by seven complete revolutions.

The motion is said to be periodic because it repeats itself over and over again after each five circuits and the length of the period is 5 circuits.

Can you find the dimensions of the tray? Is there more than one solution?
tray

To help you with this question, you may like to read the article 'A Rolling Disc - Periodic Motion'