JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD
JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B. Tech III LINEAR SYSTEMS ANALYSIS Previous Question Paper (August - 2022 - R16)
Answer any five questions. All questions carry equal marks.
Main
Obtain the state equations of the mechanical system shown figure 1 below:
Answer
For a mechanical system with mass M, spring constant K, and damping coefficient B, the motion is governed by Newton's Second Law. Let x be the displacement and v = dx/dt be the velocity. The force balance equation is:
To obtain the state equations, define state variables as x₁ = x and x₂ = dx/dt. The system of first-order differential equations is:
In matrix form, the state-space representation is:
Obtain the state-space representation of the series R-L-C circuit excited by u(t) and the response is i(t).
Answer
For a series R-L-C circuit with input voltage u(t) and current i(t), the loop equation is:
Define state variables as x₁ = ∫i dt (charge q) and x₂ = i. The derivative of x₁ is dx₁/dt = i = x₂. The derivative of x₂ is obtained from the loop equation:
The state-space representation is:
The output equation for current i(t) is:
Distinguish between static and dynamic systems with suitable examples.
Answer
Sign in to view the complete answer paper.
Obtain the state transition matrix for the following system matrix.
Answer
Sign in to view the complete answer paper.
Determine trigonometric Fourier Series of the given function.
Answer
Sign in to view the complete answer paper.
Find the Fourier transform of the following function.
Answer
Sign in to view the complete answer paper.
Show how Fourier series is used in the analysis of linear systems particularly in the analysis of electrical circuits with an example.
Answer
Sign in to view the complete answer paper.
Determine the current ‘i’ flowing through the inductor in figure 2 below for the applied voltage v(t)=10e–2t using Fourier transform.
Answer
Sign in to view the complete answer paper.
Determine the response for series RL circuit for an input of unit step signal.
Answer
Sign in to view the complete answer paper.
Write briefly about convolution integral and give its applications in Laplace transform.
Answer
Sign in to view the complete answer paper.
State and prove shifting theorem of Laplace Transform.
Answer
Sign in to view the complete answer paper.
Obtain the Laplace transform for the functions:
- i) Rectangular pulse function
- ii)
- iii)
Answer
Sign in to view the complete answer paper.
Find the relation between auto correlation function and power spectral density function.
Answer
Sign in to view the complete answer paper.
How to reconstruct a signal from its samples? Explain in detail.
Answer
Sign in to view the complete answer paper.
Find the z-transform for geometric sequence, discrete unit step and ROC for the discrete unit step function?
Answer
Sign in to view the complete answer paper.
What are the important properties for z-transforms and define them?
Answer
Sign in to view the complete answer paper.