To an input when the system has zero initial conditions) of a system to an arbitrary In short, convolution can be used to calculate the zero state response (i.e., the response The convolution integral is very important in the study of systems. Matching this with the " generic decaying oscillatory"įorm we get B=0, C=2, a=1, ω 0=3.
In this case, we can't factor theĭenominator into real factors, (so we can't use the " double exponential"įorm, but we can use the " generic decaying oscillatory"Ĭompleting the square we can rewrite the denominator If the result is in a form that is not in the tables, Put initial conditions into the resulting equation.Take the Laplace Transform of the differential equation using the derivative property.In parallel to the capacitor and inductor.Īgain, the solution can be accomplished in Spring (k=10) between the mass and a fixed support, or an induction (L=1/10) Note: we could get such a second order differential equation by adding a We could make this explicit byĪside: Origin of the Second Order Differential Equation
If the terms are not in the table, we need to