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The motion of a mass-spring system with damping is governed by y'(t) + by'(t) + 36y(t) = 0; y(0) = 1, and y'(0) =

The motion of a mass-spring system with damping is governed by y'"(t) + by'(t) + 36y(t) = 0; y(0) = 1, and y'(0) = 0. Find the equation of motion and sketch its graph for b = 0, 8, 12, and 20. What is the equation of motion for b = 0? y(t) = (Type an exact answer, using radicals as needed.)

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