Chapter 1.3, Problem 23P

(a)

To determine

To show: That the kinetic energy T of the pendulum in motion is $T=\frac{1}{2}m{L}^2{\left(\frac{d\theta }{dt}\right)}^2$.

(b)

To determine

To show: That the potential energy of the pendulum in motion is $V=mgL\left(1-\cos \theta \right)$.

(c)

To determine

The value of $\frac{dE}{dt}$ and to set that to zero to show that the resulting equation reduces to $\frac{d^{2}E}{d{t}^2}+\frac{g}{L}\sin \theta =0$.