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3. The equation of motion of a general mass-spring system subject to an external force F(t) is mx + cx' + kx = F(t) where

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3. The equation of motion of a general mass-spring system subject to an external force F(t) is mx" + cx' + kx = F(t) where m, c and k are the mass, damping coefficient and spring constant respectively. Lets consider a simple undamped system where m = 1, k = 1, and c = 0 and with forcing function F(t) = 0.5 cos(t) (all in SI units) x" + x = 0.5 cos(t) Find (the exact analytic expression for) the unique solution satisfying the initial con- ditions x(0) = x'(0) = 0 and use MATLAB to plot the function x(t) for 0

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