A single degree of freedom translational vibrating system has a concentrated mass weighing 386 lbs, a spring constant of 100 lbs./in, and a viscous damping coif. of 12 lbs-sec./in. Use Laplace transform techniques to determine the time response y(t) for a:
a. Free vibration if the initial conditions are y(0)=1 inch and y'(0)=0.
b. Forced vibration if the driving force f(t)=40sin4t pounds and the initial conditions are zero.