A fundamental model used in engineering is the forced oscillator. It arises in models ranging from automobile suspension to electric circuits. One example has a solution in the form

where is the frequency of an external force. What happens as omega gets close to 1? The bridge collapses, the washing machine goes off balance, your radio picks up a clear station, etc.

In a particular application, when , the formula for x(t) becomes

which describes oscillations with increasing amplitude. How long will it take for the amplitude to reach 100? 1,000?