Changing the Spring Consider the mass-spring system
+ + kx = 0, x(0) = 4, (0) = 0.
(a) For spring constant k = 0.25, 0.5, 1, 2, 4, the corresponding solutions are plotted together in Fig. 4.3.13. (a) Their phase-plane trajectories are plotted in Fig. 4.3.13(b). Make a trace of both graphs and label each curve with the appropriate value of k.
(b) From your observations of the graphs in Fig. 4.3.13, do the oscillations increase in frequency and amplitude as the spring constant is increased (i.e., as the spring becomes "stiffer")? Explain.

8 12 16 -4 -2 -3 b) FIGURE 4.3.13 Solutions and phase-plane trajectories for Problem 48.