A pendulum with a stiff arm (like a pen swinging from its tail) has two equilibrium points. A stable one where the tip of the pen is down, close to the surface of the Earth, and an unstable equilibrium point where the tip of the pen is up, i.e., moving far from the surface of the Earth compared to its tail. In the latter case, small oscillation around the top points are described by the equation d0 dt2 (2) where w is a constant angular frequency. Show that the solution to this differential equation is I 0 = A cosh (wt) + B sinh (wt), (3) = w0.