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Math · Advanced Math
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3. Consider the external force f(t) acting on a mechanical system for a short period of time defined as cos(2t) for 0 < t < π for t > π f(t) (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 C {f(t)), that is, the Laplace transform of the external forcing function (c) Use the Laplace transforms to solve the ordinary differential equation d2 yft) for t>o subject to the initial conditions y(0) = 0, dt t=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 [LTO]...

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