Equations of motion in the state and confiruration spaces

Consider a system with a single degree of freedom and assume that the equation expressing its dynamic equilibrium is a second order ordinary differential equation (ODE) in the generalized coordinate x. Assume as well that the forces entering the dynamic equilibrium equation are • a force depending on acceleration (inertial force), • a force depending on velocity (damping force), • a force depending on displacement (restoring force), • a force, usually applied from outside the system, that depends neither on coordinate x nor on its derivatives, but is a generic function of time (external forcing function). If the dependence of...