1 Swinging a Pendulum (18 points) Image credit: kjpargeter A pendulum has a weight of 1kg on its end; the weight of the rod is negligible. The gravity in the region is 10m/s', and the length of the rod is 1m. So if the pendulum is swinging at a rate of w (in rad/s) and is currently at an angle of d (in radians) from straight down, its total energy can be given as: E(0,w) = -10 cose + w We would like to model the swinging of this pendulum from an energy per- spective. To do this, we will note that a local minimum of energy produces what is known as a stable equilibrium: even if the pendulum is disturbed slightly, it will return to its previous state with a bit of friction (though we will assume friction is negligible for the purpose of this problem). On the other hand, any other critical point of the energy equation is an unstable equilibrium, and a pendulum in this state will only stay there until perturbed. (a) (3 points) Compute the gradient of the energy equation. Find all crit- ical points with 0