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# Springs

An astounding fraction of modern physics stems from our understanding of springs.

Which one of the following golf course contours would produce the measured net force on the ball displayed on the graph?

A wide range of materials exhibit this kind of restoring behavior: from skin, to steel beams, to the archetypal spring.

Should we expect any of these materials to follow Hooke's law exactly?

Let's look at the Florida orange from the front.
From this view it's an object that travels on a circle of radius \(r,\) with angular frequency \(\omega,\) whose position around the circle is represented by the angle \(\theta.\)

Calculate its position in the Cartesian coordinates, \(\left(x, y\right).\)

**Details and Assumptions:**

- Suppose that at time zero, the orange's angular position is \(\phi.\)

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