The Equation of Motion for the basic mass-spring-damper system with sliding friction shown below is: mx¨ + (c1 + c2) ˙x + kx = Fa(t)
(a) Apply the Laplace Transform to the equation above and solve for the variable of interest, X(s) (in
terms of the s variable). Assume m = 1 kg, c1 = 4 N-s/m, c2 = 4 N-s/m, k = 32 N/m, and Fa is a
step force with a magnitude of 8 N. (10 Pts)
(b) Determine the Inverse Laplace Transform of the equation resulting from (a) using the method of
partial fraction expansion. (15 Pts)