# The transfer function of a system is used to calculate which of the following?

### Right Answer is:

The output for any given input

#### SOLUTION

The transfer function of a linear, time-invariant system is defined as the ratio of the Laplace transform of the output to the Laplace transform of the input with all initial conditions being zero.

The transfer function is a frequency-domain concept that is used to calculate the output of the linear system to any input.

$TF = \frac{{C\left( s \right)}}{{R\left( s \right)}}$

or

**Transfer function = (Transform of o/p signal)/(Transform of i/p signal)**

**So that transfer function of the system is used to calculate the output for a given input.**

- The transfer function H(s) is defined as the ratio
**C(s)/R(s)**, where C(s) is the Laplace transform of the output signal c(t), and R(s) is the Laplace transform of the input signal r(t), and it defines the properties of the dynamic system. - The poles of the system, i.e., the roots of the denominator in H(s) give the frequencies where the system has free vibrations (if it is a transfer function of a mechanical system).
- The transfer function can (in the theoretical analysis) be used to find the solutions (responses) for any input (force) by using the inverse Laplace transform.

For unit impulse input i.e. r(t) = δ(t)

⇒ R(s) = δ(s) = 1

Now transfer function = C(s)

Therefore, the transfer function is also known as the impulse response of the system.

Transfer function = L[IR]

IR = L-1 [TF]