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For the spring-mass-damper system (refer to Ogata Figure 4.1). (i) Find the equations of motion (the differential equation). Assume m = 1, b = 7, and k = 12. 1(ii) Assuming f(t) is a step function, find the Laplacian transform, X(s). (iii) Find the time-domain solution (take the inverse transform), assuming x(0) = 3.
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