Using time moments to determine system response

Through the evaluation of the convolution of the impulse response of a system with a given forcing function, the response of the system to that forcing function can be determined. Two novel methods of obtaining the system response are presented using the time-moments of the individual elements acting on the system to determine the response of the system. Both methods presented use a Taylor series expansion of one of the two functions being convolved under the integral to obtain the response for a first-order system. In each case an algorithm is developed which shows the system response as the summation of a series of moment/derivative products. The response of higher-order systems can be obtained using these methods by decomposing them into coupled first-order systems. These two methods are easily programmed on a digital computer. A practical example is presented, and the results are compared with those obtained using the classical Laplace transform technique.<
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