##### *The Convolution Integral*

Recall that the convolution integral process is broken down into four steps:

*folding*the impulse response function:*h(tau)*folds to*h(-tau)**shifting*the impulse response function:*h(-tau)*shifts to*h(t-tau)**multiplying*the folded/shifted impulse response function with the excitation:*h(t-tau) f(tau)**integrating*to find the area under the*h(t-tau) f(tau)*curve

In the following animation, we see this four-step process to aid us in interpreting the resonance response of a single-DOF oscillator to harmonic excitation. From this, we see that the response amplitude is linearly increased as we move along in time. This is due to the lining-up of the shifted/folded impulse response function with the excitation.

**(ANIMATION AUTOMATICALLY REPLAYS)**