Enroll in one of our FREE online STEM summer camps. Space is limited so join now!View Summer Courses

### Fluid Ejection. In the design of a sewage treatme…

View
AG

Need more help? Fill out this quick form to get professional live tutoring.

Get live tutoring
Problem 20

In Project C of Chapter 4, it was shown that the simple pendulum equation
$$\theta^{\prime \prime}(t)+\sin \theta(t)=0$$
has periodic solutions when the initial displacement and velocity are small. Show that the period of the solution may depend on the initial conditions by using the vectorized Runge-Kutta algorithm with $h=0.02$ to approximate the solutions to the simple pendulum problem on [0, 4] for the initial conditions:
$$\begin{array}{l}{\text { (a) } \theta(0)=0.1, \quad \theta^{\prime}(0)=0} \\ {\text { (b) } \theta(0)=0.5, \quad \theta^{\prime}(0)=0} \\ {\text { (c) } \theta(0)=1.0,} \\ {[\text { Hint: Approximate the length of time it takes to reach }} \\ {-\theta(0) .}\end{array}$$