Multiple DOF Systems
A 1-degree-of-freedom system has 1 mode of vibration and 1 natural frequency
mpeg movie
A 2-degree-of-freedom system has 2 modes of vibration and 2 natural frequencies
mpeg movie
Note: the movie shows the two mode shapes, but does not correctly show the natural frequencies. In reality, the two modes vibrate at distinct frequencies.
A 3-degree-of-freedom system has 3 modes of vibration and 3 natural frequencies
mpeg movie
Note: the movie shows the three mode shapes, but does not correctly show the natural frequencies. In reality, all three modes vibrate at distinct frequencies.
A 4-degree-of-freedom system has 4 modes of vibration and 4 natural frequencies
mpeg movie
Note: the movie shows the four mode shapes, but does not correctly show the natural frequencies. In reality, all three modes vibrate at distinct frequencies.
A continuous system has an infinite number of vibrational modes natural frequencies
The figure at left (click on the picture to see download the mpeg movie) shows the first four mode shapes for a fixed-fixed string. This is the only animation on this page which correctly shows the different modes at their correct relative resonace frequencies. For an alternate look at the vibration of a fixed-fixed string in terms of Standing Waves see the Vibration of a Fixed-Fixed String.
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