Let \(\theta\) represent the clockwise angular displacement of the pulley of the system in Figure P1.31 from the system's equilibrium position.

(a) Express the potential energy of the system at an arbitrary instant in terms of \(\theta\).

(b) Express the kinetic energy of the system at an arbitrary instant in terms of \(\dot{\theta}\).

wwwwww FIGURE P1.31 E 2r 2 m 2 k