Acoustics and Vibration Animations
Daniel A. Russell, Ph.D.
Graduate Program in Acoustics
The Pennsylvania State University
All text and images on this page are ©2004-2011 by Daniel A. Russell
and may not used in other web pages or reports without permission.
The simplest example of an oscillating system is a mass connected to a rigid foundation by way of a spring. The spring constant k provides the elastic restoring force, and the inertia of the mass m provides the overshoot. By applying Newton's second law F=ma to the mass, one can obtain the equation of motion for the system:
The animated gif at right (click here for mpeg movie) shows the simple harmonic motion of three undamped mass-spring systems, with natural frequencies (from left to right) of ωo, 2ωo, and 3ωo. All three systems are initially at rest, but displaced a distance xm from equilibrium.|
The period of the oscillatory motion is defined as the time required for the system to start one position, complete a cycle of motion and return to the starting position.
|The movie at right (25 KB Quicktime movie) shows how the total mechanical energy in a simple undamped mass-spring oscillator is traded between kinetic and potential energies while the total energy remains constant.|