First and Second Order Systems - Classical Analysis

[mm391]

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?

 

[LabGuy330]

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.