The role of damping and initial conditions in underdamped oscillations

Abstract

The problem of underdamped classical harmonic motion through a force linearly proportional to velocity is revisited. Several properties of the system not usually studied are discussed, such as the role of constants of the displacement, the return time instants, the return positions, the maximum velocity time instants, the maximum velocity positions, the energies, the powers, and the total distance travelled. Expressions for these quantities are obtained showing the influence of the initial conditions of motion and the influence of damping.

Keywords:
Harmonic oscillator; damped oscillator; classical mechanics