Quiz MA 238-02: Pendulum Motion and Phase Portraits, Exercises of Differential Equations

Download Quiz MA 238-02: Pendulum Motion and Phase Portraits and more Exercises Differential Equations in PDF only on Docsity! MA 238-02 §4.1,4.2,4.4,6.1 Quiz #5 score Name: 17 November 1999 1. A given pendulum begins its motion from the equilibrium position with varying initial angular velocities. The resulting phase plane curves are plotted below for 0 ≤ t ≤ 15. Describe the pendulum and its motion in each of the three cases. (10 points) –6 –4 –2 2 4 6 8 10 v –2 2 4 6 8 10 12 14 16 theta 2. The graph below on the left show the solution y(t) of some differential equation. Sketch the graph of y′(t) versus y(t) (the phase portrait) on another set of axes. (10 points) –0.2 0 0.2 0.4 0.6 0.8 1 y 2 4 6 8 10 12 14t