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. |
Undamped OscillatorThe animations at left represents the motion of an undamped oscillator. The top left animation shows the object oscillating back and forth along the x-axis. The lower left animation is a plot superimposing the position x(t) as a function of time and the velocity v(t) as a function of time on the same graph. Dots have been provided to show how both the position and velocity alternate between positive and negative maximum values as the system oscillates. The combined plots also illustrate the difference in phase between position and velocity. When the position is maximum the velocity is passing through zero, and vice versa. However, the combined plot is not as easy to visualize without making it an animation. The phase-diagram plot, shown in the lower right, shows the phase relationship between velocity and position much more clearly. As the system oscillates, the phase diagram carves out a clockwise ellipse. |
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Damped OscillatorWhen the oscillator has damping, the oscillator loses energy during each cycle, and both the position and velocity decrease in amplitude as time proceeds. Graphs of position versus time and velocity versus time display an amplitude envelope which decreases exponentially. The phase-space diagram for a damped oscillator also shows that the oscillator is losing energy. As the amplitudes of the velocity and position decrease, the phase diagram spirals inwards. In classical mechanics, this is described as an "attractor" and shows that the system is trapped in a potential well from which it cannot escape. |