Response to pulse function

Only the special case of the impulse will be considered (Section 7.8.1). This is a particularly useful function for testing system dynamics as it does not introduce any further s terms into the analysis (equation 7.78). The determination of the response of any system in the time domain to an impulse forcing function is facilitated by noting that  

if the step response in the time domain is known, the impulse response can be determined by differentiating the former. 

Therefore, using equation 7.99, the response to a unit impulse is  

There are three cases to consider dependent on the form of the roots of the characteristic equation (see Fig. 7.31). 

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