Question

Find response of an undamped system initially at rest in equalibrium when the force f(t) = fo e^(-wnt) is applied

Answer 1

Finally, we solve the most important vibration problems of all.  In engineering practice, we are almost invariably interested in predicting the response of a structure or mechanical system to external forcing.  For example, we may need to predict the response of a bridge or tall building to wind loading, earthquakes, or ground vibrations due to traffic.  Another typical problem you are likely to encounter is to isolate a sensitive system from vibrations.  For example, the suspension of your car is designed to isolate a sensitive system (you) from bumps in the road.  Electron microscopes are another example of sensitive instruments that must be isolated from vibrations.  Electron microscopes are designed to resolve features a few nanometers in size.  If the specimen vibrates with amplitude of only a few nanometers, it will be impossible to see!  Great care is taken to isolate this kind of instrument from vibrations.  That is one reason they are almost always in the basement of a building: the basement vibrates much less than the floors above.

 

We will again use a spring-mass system as a model of a real engineering system.  As before, the spring-mass system can be thought of as representing a single mode of vibration in a real system, whose natural frequency and damping coefficient coincide with that of our spring-mass system.