Changing Frequencies Consider the undamped harmonic oscillator defined by + (20x = 0 with initial conditions x(0) = 4 and (0) = 0.
(a) For (0 = 0.5, I, and 2, the corresponding trajectories are plotted in Fig. 4.1 .8(a) on the same tx-plane In Fig. 4.1.8(b) the corresponding trajectories an plotted on the xi phase plane. Make a trace of bolt graphs and label each curve with the appropriate value of (0.
(b) If (0 is increased, we can see that the frequency a the oscillations in Fig. 4.1 .8(a) increases (as expected since w is the natural (circular) frequency). De scribe what happens in the phase plane (Fig.4.1.8(b). if (0 is increased. How is affected if w is increased?

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2π a) Solutions (b) Phase portraits FIGURE 4.1.8 Graphs of +매x=0(Problem 44).