### Forced oscillations

In the presence of damping, the oscillations of a system will die out in time. Therefore, a force is needed to sustain oscillations or to initiate them in the first place. That’s called a driving force, or forcing.

#### Driving forces

Driving forces can be of any form, so let’s denote them simply by f (t). This simply means that the force is a function of time without specifying the form of the force law at all.

For example, we could have a periodic force of the form F = A cos (ωt) + B sin (ωt), where A and B are constant vectors that give the amplitude (maximum magnitude) and direction of the force, and ω is the angular frequency of the forcing. This could, for example, represent an oscillator interacting with and driving another, ...

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