1. Suppose we have a uniform rod of mass M and length L that can pivot about one end. The other end is attached to a horizontal spring with constant k that is affixed to a wall. The spring is neither stretched nor compressed when the rod hangs straight down. Assume that the rod's angle from the vertical is always small and that the spring does not bend or bow. M L k A. Rigid Body: ⚫ Draw an extended body diagram for the rod as pictured above, at a small angle from equilibrium, and be sure to explicitly label any angles, forces, locations of forces, center of mass, etc. Using the forces identified in your extended body diagram, write down Newton's Second Law of Rotation for the rod. B. Oscillation: Use the small angle approximation and some algebra to rearrange your equation from the previous part so that it is of the form of equation 6.5.1 in the text: a→ d20 dt² -(constants) Deduce a symbolic expression for the angular frequency w of the pendulum using your equation of motion. See equation 6.5.2 in the text.

Fig: 1