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GATE EC 2021: Control Systems Quiz 2 (App update required to attempt this test)

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Question 1

For Passive RC low pass filter shown below,

If Vs(t) = cos(t) + cos100t, Vo(t) = α cos (t + θ) + β Cos (100 t + θ)

Then find |α||β|

Question 2

Consider the following statements:
1) The transfer function of a system is defined as the pseudo-static
relationship between the input and output variable.
2) We can compute the frequency response of an interconnected system of components with the help of Transfer functions.
3) While using the Laplace transform on a transfer function it is
possible to get information related to the qualitative behaviour of the response by solving for the dynamic response of the system
4) A transfer function is defined only for LTI systems when all initial conditions are assumed to be zero.
Which of the following are true?

Question 3

For the network shown below, find the transfer function of the system

Question 4

Determine the type and order of the system : G(s).H(s) = .

Question 5

A stable real linear time-invariant system with single pole at p, has a transfer function with a dc gain of 5. The smallest positive frequency, in rad/s, at unity gain is closest to:

Question 6

Consider a spring-mass system given as where m stands for mass, c for the damper, and spring labelled as k

In the figure shown above, consider the m= 1 units, k= 6 units, c= 8 units.
Sum of all the poles and zeroes of the transfer function is:
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