Open Educational Resources

Vibrations and Sound: Transient Vibrations

As we have discussed so far, in many situations the long term (steady state) response of a vibrating system is of interest. For example, for a motor that will operate more than 99% of the time at a fixed operating speed we would typically want to investigate the response at that speed so an appropriate vibration isolation system could be designed.

On the other hand, there are times when it is the {transient} response of the system that is of interest.

  • item For the motor example above, we may be concerned about the response at startup, particularly if the system passes through resonance.
  • item The response of an automobile suspension system when a pothole or other obstacle in the road is encountered.
  • item The response of various mechanical systems to shock loading.

In these situations, the loading isn’t periodic or is applied for a short period of time. We will look at the responses for some specific examples. We will limit ourselves generally to undamped systems for simplicity so that the general form of the equation of motion we are concerned with here is

(1)   \begin{equation*} 	m \ddot{x} + k x = F(t) \end{equation*}

where F(t) is the disturbing force under consideration.

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