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  3. 3 consider the external force ft acting on a mechanical...

Question: 3 consider the external force ft acting on a mechanical...

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3. Consider the external force f(t) acting on a mechanical system for a short period of time defined as f(t)-, cos(2t) for 0 < t < π for t > π (a) Write the external force f(t) in terms of the unit step function (the Heaviside function) u(t) as defined in the lecture notes chapter Step functions and t-shifting. (b) Evaluate (t)), that is, the Laplace transform of the external forcing function. (c) Use the Laplace transforms to solve the ordinary differential equation y f(t) for t>o dt2 subject to the initial conditions dy dt y(0) = 0, -1 1-0 and f(t) is the external force function defined above. Write the final solution as a piecewise function. Show all working and clearly state each Laplace transform property/rule used Note: When stating each Laplace transform property/rule you can refer to the row number in the Laplace transform table on the formulae sheet, for example: First we apply the Laplace transform to the function y(t) by using [LT)...

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