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. |

In order for mechanical oscillation to occur, a system must posses two quantities:

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:

where

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 ω_{o}, 2ω_{o}, and 3ω_{o}. All three systems are initially at rest, but displaced a distance x from equilibrium._{m}
The ⇒ From the position versus time plot, can you determine the period for each of the three oscillators? |

The elastic property of the oscillating system (spring) stores potential energy

and the inertia property (mass) stores kinetic energy

As the system oscillates, the total mechanical energy in the system trades back and forth between potential and kinetic energies. The total energy in the system, however, remains constant, and depends only on the spring contant and the maximum displacement (or mass and maximum velocity

The movie at right (25 KB
Quicktime movie) shows how the total mechanical energy in a simple undamped mass-spring oscillator is traded between and kinetic energies while the total energy remains constant.
potential |