JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III LINEAR SYSTEMS ANALYSIS Previous Question Paper (February - 2023 - R16)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
PART - A
What is state space representation?
Answer
State space representation is a mathematical model of a physical system as a set of input, output, and state variables related by first-order differential equations. It represents a system in the time domain using a vector-matrix form, typically expressed as:
where x is the state vector, u is the input vector, y is the output vector, and A, B, C, D are the system, input, output, and feedforward matrices respectively.
What are natural state variables for electrical and mechanical systems?
Answer
Natural state variables are physical quantities that represent the energy storage elements of a system. For electrical systems, the natural state variables are the inductor current (i_L) and the capacitor voltage (v_C), as these variables uniquely determine the energy stored in the magnetic and electric fields, respectively.
For mechanical systems, the natural state variables are displacement (x or θ) and velocity (v or ω). Displacement represents the potential energy stored in springs, while velocity represents the kinetic energy stored in masses or moments of inertia.
Define wave symmetry.
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Find the Fourier transform of exp (-ax2).
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State Strums’ theorem.
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What is Hurwitz polynomial?
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How do we do impulse sampling?
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What is a band limited signal?
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State the fundamental difference between continuous and discrete time signals.
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List the Periodicity Properties of Discrete-time Complex Exponentials.
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PART - B
Using equivalent source method write the normal form state equation in vector form for the circuit shown below figure 1.
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Distinguish between static and dynamic systems with suitable examples.
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Obtain the state-space representation of the series R-L-C circuit excited by e(t) and the response is i(t) (figure 2).
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Obtain the trigonometric Fourier series expansion of the periodic triangular waveform shown in figure 3.
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Obtain the exponential form of Fourier series of the unit impulse function shown in figure 4.
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State and explain the properties of Fourier Transform.
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Define Signum function and hence develop the expression for Fourier transform of it.
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Find the Laplace transform of a periodic waveform shown in the figure 5.
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Find the inverse Laplace transforms f(t) using convolution integral for the function F(s) = 3 / ((s+1)(s+4)).
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Find the expressions for the current i(t) in a series R-L-C circuit, with R=5Ω, L=1H, C=1/4 F, when it is fed by a ramp voltage of 12 r(t-2).
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Distinguish between unit impulse function and unit doublet function and hence develop the Laplace transform of these functions.
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Explain Band Pass sampling of functions with examples.
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Explain Cross correlation and auto correlation of functions.
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What is sampling and reconstruction? Explain.
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How can the signal be reconstructed from the samples? Explain briefly.
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Distinguish between Laplace , Fourier and Z Transforms.
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What are the constraints of ROC on various classes of signals?
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What are the properties of Z Transforms?
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How do you find the inverse of Z transforms of F(z) = z / ((z-1)(z-2)).
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