ABSTRACT
The linear growth of amplitude, for undamped resonance, would be limited by non-linear effects in the restoring force, once the displacement becomes large. The example of damped or amplified oscillators with forcing include the analogous mechanical system. The methods used to study the basic harmonic oscillator are the basis for the extension to higher-order discrete or continuous systems with more independent and dependent variables. The simplest mechanical system consists of a mass and spring, conserving the total energy in the absence of external forcing; the free motion is an oscillation with constant amplitude around the position of stable equilibrium. The energies corresponding to the inertia force are the kinetic energy, whose sum is the total energy; the latter is dissipated by friction whereas applied forces may have no effect or increase or decrease the total energy.
