1. Walk before you run. (10 points: 5+5) When you walk, one foot and leg acts as an inverted pendulum, while the other swings as a free pendulum.

a) Considering the free pendulum leg, estimate the interval between footfalls you expect for your leg (try this carefully, considering realistic moments of inertia and center of mass positions for your leg). Time steps of your natural walk to check your answer (you should be able to get within 10 or 15% with elementary physics beyond OoM).

b) An upper limit to the walking speed is set by the inverted pendulum leg: what is the maximum speed at which you could walk without that leg being lifted off the ground by centrifugal acceleration? Compare this speed to one you estimate from the "natural pendulum" of part (a) and your natural step length. [humans have two gaits: walking, where only one foot is lifted at a time, and running, where both feet are sometimes off the ground. 4-legged animals like horses have more gaits, depending on whether 1, 2, 3 or 4 feet are off the ground: walk, trot, canter, gallop respectively.]