Chapter 12.18, Problem 6P

For the initial conditions $\theta ={\theta }_0,\stackrel{\dot{}}{\theta }=0,$ show that the constants $A$ and $B$ in equations (18.6) and (18.7) are as given in (18.8). Hints: Show that $d\theta /du$ = 0 if $\stackrel{\dot{}}{\theta }=0.$ In equations (18.6) and (18.7), set $\theta ={\theta }_0$ and $d\theta /du=0$ when $u=u_0$ and solve for $A$ and $B$.

Then use the formula in Problem 5 to simplify your results to get equation (18.8)