The gravitational potential energy of a pendulum is U = mgy?
(a) Taking y = 0 at the lowest point, show that y = L (1 − cos (), where ( is the angle the string makes with the vertical.
(b) If ( is small, (1 - cos () ≈ 1/2 (2 and ( ≈ x / L (Appendix A.7). Show that the potential energy can be written U ≈ 1/2 kx2 and find the value of k (the equivalent of the spring constant for the pendulum)?