obtain C. a. Natural frequency wn and damping ratio b. Damped frequency wa if applicable, and...
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obtain C. a. Natural frequency wn and damping ratio b. Damped frequency wa if applicable, and second order system time constant Using Laplace transforms, obtain the characteristic polynomial of the system, and find its roots. For each case, state, based on the roots (or, based on < value) whether the system is underdamped, critically damped, or overdamped. Using the solution template posted under Lecture 23, obtain the free response for each case, and plot the free response. Your plot should include axes labels, relevant information at time t = 0 and the general shape of the system response. d. For each of the three second order systems, e. 4y + 16ý + 32y = 0, y(0) = 1, y(0) = -2 3z + 24ż + 36z = 0, z(0) = -1, ż(0) = 0 5x + 20x + 20x = 0, x(0) = 0, x(0) = 1 obtain C. a. Natural frequency wn and damping ratio b. Damped frequency wa if applicable, and second order system time constant Using Laplace transforms, obtain the characteristic polynomial of the system, and find its roots. For each case, state, based on the roots (or, based on < value) whether the system is underdamped, critically damped, or overdamped. Using the solution template posted under Lecture 23, obtain the free response for each case, and plot the free response. Your plot should include axes labels, relevant information at time t = 0 and the general shape of the system response. d. For each of the three second order systems, e. 4y + 16ý + 32y = 0, y(0) = 1, y(0) = -2 3z + 24ż + 36z = 0, z(0) = -1, ż(0) = 0 5x + 20x + 20x = 0, x(0) = 0, x(0) = 1
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