The displacement x(t) cms at time t seconds, of a spring moving along a line is given by the formula: x(t) = 8e- cos(2t). Compute the velocity x'(t) and acceleration x"(t) of the spring and show that these are related by a formula of the kind x" + ax' + bx = 0 for suitable constants a and b which must be found. Also estimate the maximum speed of the particle and its maximum acceleration, during its motion, with explanation. Also discuss the behavior of the motion for large times.

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