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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.


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1 Answer 1

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.

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