Example 4.  Compare the graphs of the solutions to  
(i)          with  ,   ,    
    and
(ii)          with  ,   .    

Solution 4.

From the graph's can you tell which is the solution to (ii)?  How?

The differential equation in example 3 is called the nonlinear pendulum.

Is is a better model that the one given in example 1.

(c) John H. Mathews 2004