The gravitational potential energy of a pendulum is U = mgy. 

(a) Taking y = 0 at the lowest point, show that y = L(1 − cos θ), where θ is the angle the string makes with the vertical. 

(b) If θ is small,and θ ≈ x/L (Appendix A.9). Show that the potential energy can be written and find the value of k (the equivalent of the spring constant for the pendulum).

Transcribed Image Text:

(1 cos 0) ơ