SDOF Systems under Harmonic Excitation |

When a SDOF system is forced by
When the forcing function is
Consider the SDOF system forced by the harmonic function
The particular solution for this problem is found to be,
The general solution is given by the sum of the complimentary and particular solutions multiplied by two weighting constants
The values of |

Undamped SDOF Systems under Harmonic Excitation |

For an undamped system (
If the forcing frequency is close to the natural frequency, , the system will exhibit
When the forcing frequency is equal to the natural frequency, we cannot use the
To simplify x(t), let's assume that the driving force consists only of the cosine function, ,
The displacement solution reduces to,
This solution contains one term multiplied by
The maximum displacement of an undamped system forced at its resonant frequency will increase unbounded according to the solution for |