An object of mass \(m\) can move in two dimensions in response to the simple harmonic oscillator potential \(U=(1 / 2) k r^{2}\), where \(k\) is the force constant and \(r\) is the distance from the origin. Using the Jacobi action, find the shape of the orbits using polar coordinates \(r\) and \(\theta\); that is, find \(r(\theta)\) for the orbit. Show that the shapes are ellipses and circles centered at the origin \(r=0\).