Problem 3. A Pendulum We analyze a simple pendulum, as shown in Figure 3, in a rotating coordinate frame. Figure 3. A simple pendulum is made up of a mass m hanging from a massless string with length L. The inertial coordinate frame is shown here with coordinate axes x and y. The z-axis points out of the plane of the drawing through the origin O. A rotating coordinate frame spins about the z-axis and has the same origin O, with coordinate axes coinciding with the x axis and the y axis at / = 0. At f = 0, the mass m is located at 0 = 0, moving in the direction of positive 0. The period of the pendulum is P. The rotating coordinate frame spins around the z axis with constant angular velocity vector W = P Draw a free-body diagram that shows all applicable forces, including inertial forces, in the rotating coordinate frame at t = P/4