(a) A system is described in the time domain by the equation: *(t) + 10x(t) + 30x(t) = u(t) Assume that all initial conditions as zero. Find the transfer function of this system, and the steady-state response for an impulse input using the Final Value Theorem. (i) r. Find the time domain response of the system for an impulse input and verify that the response as t → o is the same as that given by the Final Value Theorem. (ii)

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Q1
(a)
A system is described in the time domain by the equation:
*(t) + 10x(t) + 30x(t) = u(t)
Assume that all initial conditions as zero.
Find the transfer function of this system, and the steady-state response
for an impulse input using the Final Value Theorem.
(i)
r.
Find the time domain response of the system for an impulse input and
verify that the response as t → o is the same as that given by the Final
(ii)
Value Theorem.
The Frequency response of a system can be obtained experimentally or
theoretically. Briefly explain both approaches. Which are the two common
methods to represent the frequency response graphically?
(b)
Give a definition of a root-locus diagram. In your answer, explain what is
meant by characteristic equation and discuss its significance in this context.[5
Transcribed Image Text:Q1 (a) A system is described in the time domain by the equation: *(t) + 10x(t) + 30x(t) = u(t) Assume that all initial conditions as zero. Find the transfer function of this system, and the steady-state response for an impulse input using the Final Value Theorem. (i) r. Find the time domain response of the system for an impulse input and verify that the response as t → o is the same as that given by the Final (ii) Value Theorem. The Frequency response of a system can be obtained experimentally or theoretically. Briefly explain both approaches. Which are the two common methods to represent the frequency response graphically? (b) Give a definition of a root-locus diagram. In your answer, explain what is meant by characteristic equation and discuss its significance in this context.[5
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