ABSTRACT
For the system in Fig. 1, F ma yields its differential equation of motion, as follows.
mx¨ cx˙ kx ƒ(t) (2) For the system in Fig. 1, the forces acting upon the mass include the exter-
nally applied time-dependent force, ƒ(t), plus the spring and damper motion-de-
spring force resisting displacement (x) in either direction from the equilibrium position and the damper force resisting velocity (x˙) in either direction. The weight (mg) and static deflection force (kst) that the weight causes in the spring cancel each other. Equations of motion are generally written about the static equilibrium position state and then need not contain weight and weight-balancing spring deflection forces.
