ME 482

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Transient Vibrations of Single Degree of Freedom
Systems
Single Degree of Freedom System with an applied
force f(t)
where f(t) can be of any form.
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Equation of Motion
Solution
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Solution for a General Force F(t)
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Example
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Excitations Changing at Discrete Times
A step force f(t) starting at t 0
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A step force f(t) starting at t t0
In general, we have the convolution integral
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Some Excitations Given in Figure 4.5
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Response of an Undamped Single-Degree-of-Freedom
System
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Transient Motion due to Base Excitation
x Displacement of system y Displacement of base
Equation of Motion
Defining z x - y, we get
Or,
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Solution with Convolution Integral