Horizontal Spring-Mass Simulator

The motion of a horizontal spring–mass system is modeled by a 2nd-order linear homogeneous ODE, where x is the mass's displacement from equilibrium at time t. It comes from Newton's second law applied to the net force on the mass: the spring's restoring force, given by Hooke's law, plus a damping force proportional to velocity, such as air resistance or a mechanical damper resisting the motion. Because the mass moves horizontally, its weight is canceled by the normal force from the floor, so gravity does not enter the equation of motion; the floor is also assumed to be smooth, so it contributes no friction of its own.