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Consider a second-order process, where the transfer function is given by ... , where ... is the process time constant and ... is the damping coefficient. This Demonstration shows the response of this process when subject to a step input of amplitude ... (i.e., ... , where ... is the unit step function) or an impulse input of amplitude ... (i.e., ... , where ... is the Dirac delta function). The response is obtained by Laplace inversion using the Mathematica built-in function, ... . When ... , one gets an underdamped response with oscillatory behavior. Critically damped and overdamped systems result when ... and ... , respectively. For these last two cases, the response does not exhibit oscillations. A critically damped response returns to steady state faster than an overdamped response when the system is subject to an impulse input.
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