3. A long rod hangs on a peg. The rod has a total length L and mass M. The peg is located a distance 5 above the center of mass of the peg. This is shown to the right. [15 points] a. Derive the equation for the period of the rod. Simplify your equation as much as you . can. Your equation should only involved values dened in the problem, numbers, and physical constants. [5 points] In homework 2, we found an equation for the moment of inertia for a rod rotating L _ around a point at a distance s from the center. You may use the result of that question if you need it. For parts b-d, your instructor built this physical pendulum in your pre-class videos for lecture 4.3 (see videos 0.1-3 in the youtube playlist linked here). The yard stick he used as the rod is 91cm long. b. Use your equation to predict the period of oscillation when axis is 7.60m (3in) from the center of the rod. [3 pts] c. Use your equation to predict the period of oscillation when axis is 380m (1 Sin) from the center of the rod. [3 pts] d. Calculate the percent error between your predicted periods and the measured periods for both locations of the axis. The measured periods are give in the linked videos or in the lecture slides posted to Canvas from that class. [4 points]