The equation x″ - ax′ - b(x′)3 - kx was devised by Lord Rayleigh to model the motion of the reed in a clarinet. With a = 5, b = 4, and k = 5, solve this equation numerically with initial conditions x(0) = A, and x′(0) = 0 over the interval [0, 10] for the three choices A = 0.5, 1, and 2. Use MATLAB’s hold command to prepare both time plots and phase plane plots containing the solutions to all three initial value problems superimposed. Describe the relationship that you see between the three solutions.
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