### Time Domain Analysis

Time Response:
Time Response is the output which is given as a function of time when an input signal is applied. Time Response of a system can be split into two different parts:

1. Transient Response

Time Response of a control system can be represented as:

Mathematically Time response can be depicted as:

$\small \;\;c(t)\;=\;c_t(t)\;+\;c_{ss}(t)$

Where,
$\small c_t(t)$= transient response
$\small c_{ss}(t)$= steady state response

Transient Response:
Transient response is the part of the response in the transient state. It is ideally 0 and practically decreases with increasing time.
I.e $\small lim_{t\rightarrow\infty}c_t(t)=0$

Transient response can be exponential or oscillatory in nature.