(a) Show that x(t) given in part (a) of Problem 39 can be written in the form

When is small, the frequency of the impressed force is close to the frequency v_2p of free vibrations. When this occurs, the motion is as indicated in Figure 5.1.22. Oscillations of this kind are called beats and are due to the fact that the frequency of sin _t is quite small in comparison to the frequency of sin gt. The dashed curves, or envelope of the graph of x(t), are obtained from the graphs of Use a graphing utility with various values of F0, _, and g to verify the graph in Figure 5.1.22.

Reference : problem 39

(a) Show that the solution of the initial-value problem

Step 1:

In this question, we have to show that x(t) given in part (a) of Problem 39 can be written in the form

Step 2:

By using the trigonometric formula

According to the formula