On the Vibration Statistics of a Randomly Excited Hard-Spring Oscillator

Abstract

The system considered is a harmonic oscillator with a hard spring excited by random noise of the “infinitesimal impulse” type. An expression for the joint density of displacement and velocity is obtained and from this; the distributions of displacements and extrema and the average number of zero crossings are found. In addition, by solving a fundamental integral equation, we are able to find the shape of the distorted sine wave “carrier” for finite amplitude vibrations.