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## Homework Statement

A particle moves periodically around an ellipse of equation ##\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1##. You can assume ##a>b##. The ##x## and ##y## components of the particle's velocity can never exceed ##v## at any point. What is the minimum possible period of the periodic motion of the particle?

## Homework Equations

Motion in an ellipse. Kinematics.

## The Attempt at a Solution

It seems I could divide the ellipse into sectors and come up with constraints for the time the particle takes to travel in those sectors. I am not sure though how?

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