Meaning of time constants in signals (Laplace Domain)


Thread Starter


Dear All,

When I have a equation 1/sT
its an integrator with time constant
i.e Assuming a T of 5s, if I input a unit step function, the output of the integrator reaches unity in 5 seconds

at least I understand it that way. Please correct me if I am wrong
in the same way can someone help me to understand the physical meaning of T in the following equation

Signal = 1/(1+sT) and Signal = 1/(1+ s*T1 +s^2*T2)
also kindly help me to find the lapalace inverse of the above signals!
this second year university stuff, but any engineering handbook will help.

forget the complex plane solutions, just think in terms of the time responses of your inputs and equipment response and go from there.

you might also do a search for the dynamic response of linear second order systems. they may even have some nice simulations for you to play with.
Radhakrishnan... if I have interpreted your query correctly, then it seems like you need an Inverse LaPlace Transform refresher. You have confused constants in the Laplace domain with time-constants in the time domain. Following is a discussion on your three problems:

(a) ILP{1/s*T}=K*ILP{1/s}, then in the time domain, f(t)=K*1, wich is a step-function having a magnitude, K=1/T.

(b) ILP{1/(1+s*T)} which is of the form ILP {K*[1/(s-a)]}, and in the time domain, f(t)=K*EXP(a*t).

(c) ILP{1/(1+T1*s+T2*s^2)}=ILP{1/(A*s^+B*s+C)} which is of the form ILP{1/[(s+a)*(s-a)]}=ILP{1/(s^2-a^2)}, then in the time domain, f(t)=[Sinh(a*t)]/a.

Radhakrishnan... a caveat!

Because Problem (c) involves a Quadratic Equation, having constants A, B, and C, then, how does one know if the answer is complex or not? Here is a quick trick... it is complex if the ratio, (C/B)/(B/A), is greater 0.25!

Note: I leave the determination of the constants to you. However, I will provide additional help if needed.

Regards, Phil Corso