# Transfer Functions Examples Part 1

1) The impulse response of a system is
What will be the transfer function of the system?

Answer
For impulse response, the output C(s) of the system is equal to transfer function of the system.

Therefore, transfer function of the system is 2) Find the poles and zeros of the function Answer

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3) The poles and zeros are plotted on the is plain as shown below Find the transfer function. Answer Here, the poles are s = - 3, - 1, 0. Therefore, denominator of the function would be, the zeros are, -4, - 2.

Therefore, numerator of the function would be,
Therefore, transfer function would be,
Where, K is the gain factor of the control system.

4) Find the gain factor K of a transfer function whose value is 2 at s = 2 and the transfer function is given as
Answer
Now, as per condition of the problem,

5) Find the transfer function of the following network.
Answer
From the circuit we get,
Now applying Laplace transformation at both sides we get,
As the applied voltage is cause and the corresponding charging current is the effect, the applied voltage can be considered as input and charging current can be considered as output.
6) Find the transfer function of the network given below,
Answer
In the above figure the input is applied voltage v(t) and the output is measured as the voltage appears across the capacitor C that is v_{c}(t).
Laplace transformation of the transfer function is
7) A shaft of innertia J is rotated for an angle θ due to applied torque T against a bearing friction f. Find the transfer function of the system.
Answer
The differential equation form of the above statement is
Taking Laplace transformation of both sides of the system,
As the applied torque is input and the output angular displacement is output of the system.

8) The impulse response of the system is given by c(t) = 1 - te^{-2t} + sin3t. Find that transfer function of the system

Answer
9) Find the transfer function of the impulse response of a system given by
Answer