Consider the damped problem using the parameter values L
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Consider the damped problem using the parameter values L = 1, m = 1, ? = 0.1, and k = 1. (a) Use a computer to draw a di
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Consider the damped problem using the parameter values L = 1, m = 1, ? = 0.1, and k = 1. (a) Use a computer to draw a direction field of the corresponding dynamical system. (b) If you have access to computer software that is capable of solving event problems, solve for and plot the graphs of x(t) and x? (t) for the following sets of initial conditions: i. x(0) = 2, x? (0) = 0 ii. x(0) = 5, x? (0) = 0 Give a physical explanation of why the limiting values of the trajectories as t ? ? depend on the initial conditions. (c) Draw a phase portrait for the equivalent dynamical system.
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