8. Consider the motion of a simple pendulum mgsin(0 mg mgcos(0) The restoring force is mg sin 0 and hence the governing equation is mL dt2 + mg sin (0) = 0 Let the length of the string be g. Hence, the governing equation simplifies to + sin (0) = 0 dt? At the initial time, the pendulum is pulled to an angle of 0 = 30° = before being let loose without any 6. velocity imparted. Write a code to solve for the motion of the pendulum till t = 100 seconds using (a) Forward Euler (b) Backward Euler (c) Trapezoidal Rule • Recall that you need to need to reformulate the second order differential equation as a system of first order differential equation. • Vary your time step At in {0.01,0.02, 0.05, 0.1,0.2, , 0.5, 1,2, 5, 10, 20}. • For each At plot the solution obtained by the three methods on a separate figure till the final time of 100. • Discuss the stability of the schemes. From your plots, at what At do these schemes become unstable

8. Consider the motion of a simple pendulum mgsin(0 mg mgcos(0) The restoring force is mg sin 0 and hence the governing equation is mL dt2 + mg sin (0) = 0 Let the length of the string be g. Hence, the governing equation simplifies to + sin (0) = 0 dt? At the initial time, the pendulum is pulled to an angle of 0 = 30° = before being let loose without any 6. velocity imparted. Write a code to solve for the motion of the pendulum till t = 100 seconds using (a) Forward Euler (b) Backward Euler (c) Trapezoidal Rule • Recall that you need to need to reformulate the second order differential equation as a system of first order differential equation. • Vary your time step At in {0.01,0.02, 0.05, 0.1,0.2, , 0.5, 1,2, 5, 10, 20}. • For each At plot the solution obtained by the three methods on a separate figure till the final time of 100. • Discuss the stability of the schemes. From your plots, at what At do these schemes become unstable

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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