For the initial value problem in 13, plot u_ versus u for = 0.7, = 0.8, and = 0.9

Chapter 3, Problem 15

(choose chapter or problem)

For the initial value problem in 13, plot u_ versus u for = 0.7, = 0.8, and = 0.9. (Recall that such a plot is called a phase plot.) Use a t interval that is long enough so that the phase plot appears as a closed curve. Mark your curve with arrows to show the direction in which it is traversed as t increases. 16 through 18 deal with the initial value problem u__ + 1 8 u_ + 4u = F(t), u(0) = 2, u_(0) = 0. In each of these problems: G a. Plot the given forcing function F(t) versus t, and also plot the solution u(t) versus t on the same set of axes. Use a t interval that is long enough so the initial transients are substantially eliminated. Observe the relation between the amplitude and phase of the forcing term and the amplitude and phase of the response. Note that 0 =_k/m = 2. G b. Draw the phase plot of the solution; that is, plot u_ versus u.