Imagine that a block of mass 1 kg is attached to a ceiling by a spring with constant 5 kg/s? and a damper with constant 2 kg/s, and subjected to a force f(t), measured in Newtons (that is kgm/s²). Then its displacement from equilibrium in meters obey the equation dx + 2 +5x = f(t). dt dt2 Let f(t) = 3 eat and let initial conditions x(0) = x'(0) : = 1. Solve the DE for a = -2, and a = 2. [Hint: It is strongly recommended you solve for the general solution and IC-determined constants first, in terms of a. Then plug in to get the specific solution for each case.]

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