Solved: (a) Show that x(t) given in part (a) of can be written in the form . (b) If we

Chapter 5, Problem 41

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(a) Show that x(t) given in part (a) of can be written in the form . (b) If we define , show that when # is small an approximate solution is . When # is small, the frequency g2p of the impressed force is close to the frequency v2p 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 (F0 2#g) sin #t. Use a graphing utility with various values of F0, #, and g to verify the graph in Figure 5.1.22.