ANALYSIS OF DAMPED HARMONIC OSCILLATOR BY MATRIX METHOD

The motion of damped harmonic oscillator capable of oscillating in a medium such as air, water etc. is always opposed by the frictional (or damping) forces which arise from the resistance of the medium or from within the system itself and act opposite to direction of the motion of the body and result in the decrease in the amplitude of the oscillations with time. As a result of the decrease in the amplitude of the oscillations, there is a dissipation of energy of the oscillations and ultimately, the body stops oscillating. The analysis of damped harmonic oscillator is generally done by adopting the classical method. In this paper, we analyze the response (behaviour) of a damped harmonic oscillator by solving its differential equation by the matrix method. The response obtained will provide an expression for the displacement of the damped oscillator from the equilibrium position at any instant. The behaviour of the displacement obtained is determined by the damping factor and the stiffness factor