4. (20 points) Consider the following simple spring mass system. By applying F = ma, we can obtain the following second order differential equation. mä + kx = 0 (2) where m is the mass of the object attached to the spring and k is the spring constant. (k > 0) Imm F (a) Let X(s) = L(r(t)), r(0) = 0 and (0) = v. Find X(s) in terms of v, s, k and m. (b) By using X(s), find a(t). m

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