How can I obtain the time constant of the transfer function of a first order system, such as the example below?
$$ \frac{C(s)}{R(s)} = \frac{2}{s + 3}$$
Where $C(s)$ is the output of the system and $R(s)$ is the input of the system.
I'm not looking for an exact answer, I just would like to be pointed in the right direction as to how to solve for the time constant so that I can solve it myself.
Thanks.
Best Answer
The LTI system whose transfer function is
$$H (s) = \frac{2}{s + 3}$$
has the impulse response
$$h (t) = 2 \, e^{-3 t} = 2 \, e^{- t / \tau}$$
where $t \geq 0$ and $\tau := \frac{1}{3}$ is the time constant. I am assuming that the system is causal, of course.