# First and Second Order Systems - Classical Analysis

by mm391
Tags: analysis, classical, order, systems
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 P: 63 This was a lecture example and it has confused me. Can someone please help explain it? If we have the following fist order system: τ.dx/dy+y(t)=x(t) where τ=c/k where "k" is the spring stiffness and "c" the linear damper coefficient and τ is a time constant. For the unforced case x(t)=0, we need to write down an expression for the response when the initial condition is y(0)=y0. ANd how do we sketch the repsonse?
 P: 37 I have to clarify something before giving any advisement. Are you sure the differential equation is what you have provided or is it: τ.dy/dt + y(t) = x(t) The reason I ask is the above equation represents a first order spring-damper system where τ = (dampening coefficient/spring stiffness), as you stated.

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