A rigid bar pendulum is attached to a cart, which moves along the horizontal plane. The rigid bar has a center of mass at L/2. The pendulum is pinned to the cart, and a torsional spring is located between the cart and the pendulum. Assume the torsional spring does not cause a dynamic effect on the cart (but does affect the rigid bar). Recall for a pinned attachment we can assume reaction forces in the horizontal and vertical directions. There is a horizontal force F(t) that acts on the cart, which is also attached to a wall on the opposite side through a linear spring. Ignore friction.

a. Identify the number of degrees of freedom, and define a choice of generalized coordinates.
b. Find the equations of motion using Newton's second law.