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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?

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