The nonlinear mass-spring system is described by the second order differential equation: mx + k(x +...
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The nonlinear mass-spring system is described by the second order differential equation: mx + k(x + ßx³) = 0, where m, k and ß are constants and the displacement x is a function of time t. 4.1. (5 marks) Work out and state the algorithmic equations for applying the symplectic Euler method to solve equation (2). 4.2. (5 marks) Show how your MATLAB function from Task 1 can be adapted to account for the additional parameter B. (2) 4.3. (20 marks) Write a MATLAB program to create a plot comparing the displacement versus time calculated by (a) the symplectic Euler method with 200 time steps and (b) MATLAB's ode45. Use the parameter values given on page 1. Include the plot in your report and describe your observations. The nonlinear mass-spring system is described by the second order differential equation: mx + k(x + ßx³) = 0, where m, k and ß are constants and the displacement x is a function of time t. 4.1. (5 marks) Work out and state the algorithmic equations for applying the symplectic Euler method to solve equation (2). 4.2. (5 marks) Show how your MATLAB function from Task 1 can be adapted to account for the additional parameter B. (2) 4.3. (20 marks) Write a MATLAB program to create a plot comparing the displacement versus time calculated by (a) the symplectic Euler method with 200 time steps and (b) MATLAB's ode45. Use the parameter values given on page 1. Include the plot in your report and describe your observations.
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Related Book For
Numerical Methods For Engineers
ISBN: 9780071244299
5th Edition
Authors: Steven C. Chapra, Raymond P. Canale
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