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Vibrations
Free Forced
Undamped Damped Undamped Damped
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.
Equation of Motion:
Solution:
Solution for a General Force F(t):
Example:
Excitations Changing at Discrete Times:
A step force f(t) starting at t = 0:
A step force f(t) starting at t = t0:
In general, we have the convolution integral:
Some Excitations Given in Figure 4.5:
Response of an Undamped Single-Degree-of-Freedom System: