Question 11 pts
x(t) is a time domain function. The laplace transform of x(t) is in what domain:
s domain
none of the above
f domain
time domain
Flag this Question
Question 21 pts
if X(s) is the Laplace transform of x(t), then 's' is a :
real number
integer
complex number
rational number
Flag this Question
Question 31 pts
In a unilateral Laplace transform the integral, the start time is
just after origin (0+)
just before origin (0-)
origin
negative infinity
Flag this Question
Question 41 pts
For a given x(t), how many X(s) are possible:
0
many
2
1
Flag this Question
Question 51 pts
The Laplace transform of a unit step function is :
s
1
1/s
0
Flag this Question
Question 61 pts
Laplace transform of an impulse function is:
1/s
s
1
0
Flag this Question
Question 71 pts
Which of the following properties Does Laplace transform not follow:
linearity
non-linearity
time scaling
multiplication by a constant
Flag this Question
Question 81 pts
time shift in time domain leads to :
frequency shift in s domain
differentiation in s domain
none of the above
multiplication by an exponential function in s domain
Flag this Question
Question 91 pts
In a strictly proper rational function:
m = n
none of the above
m < n
m > n
Flag this Question
Question 101 pts
For a stable system, all the poles of the transfer function are:
in the right hand plane
in the left hand plane
at the origin
on the x axis
Flag this Question
Question 111 pts
The ratio of the output of a system to the input in s-domain is called:
poles
none
the transfer function
frequency response
Flag this Question
Question 121 pts
If the transfer function is an improper rational function, when is the system stable?
if there are no poles
never
if the transfer function is a constant
if poles are in the left hand plane
Question 11 pts x(t) is a time domain function. The laplace transform of x(t) is in...
Question 17 1 pts Knowing the transfer function of a system is useful because: O It helps us calculate the weight of the system It does not really help us! It helps us find the response to any input function It helps us calculate the heat transferred by the system Question 18 1 pts A system is BIBO stable if all the poles of the transfer function (given that it is strictly proper rational) reside in: The origin The right...
Question 11 1 pts An LTI system is BIBO stable if and only if the impulse response h(t) is: Discrete Differentiable Continuous Absolutely integrable Question 12 1 pts Frequency shift in S domain results in: None of the above Ist derivative in time domain Integral in time domain Multiplication by an exponential function (e-at) in time domain
Question 35 1 pts Shift in time domain results in: Convolution in frequency domain Multiplication by an exponential function in frequency domain None of the above No change in frequency domain
Question 13 1 pts Multiplication in the time domain is: 1st derivative in frequency domain Addition in frequency domain Multiplication in frequency domain Convolution in frequency domain Question 14 1 pts Laplace and Fourier transforms convert integro-differential equations in time domain to None of the above Trigonometric equations Logarithmic equations Algebraic equations
Purpose: Use Laplace transforms to find the time domain response of a RLC band-pass filter to step and impulse inputs Vout Vin L=27 mH For the RLC circuit above Find the s-domain transfer function: Find the impulse response h(t) H(s) = Vout(s)/Vin(s) · These operations must be performed by hand using Laplace transforms, do not use MATLAB or a circuit simulator. We will verify your hand calculations in lab. Hints: To find the transfer function, find the equivalent impedance of...
Question 9 3 pts The Laplace transform of the piecewise continuous function 4, 0<t <3 f(t) is given by t> 3 (2, L{f} = { (1 – 3e-*), s>0. O 2 L{f} (2 - e-st), 8 >0. 2 L{f} = (3 - e-st), s >0. O None of them 1 L{f} (1 – 2e -st), s >0.
A continuous-time LTI system has unit impulse response h(t). The Laplace transform of h(t), also called the “transfer function” of the LTI system, is . For each of the following cases, determine the region of convergence (ROC) for H(s) and the corresponding h(t), and determine whether the Fourier transform of h(t) exists. (a) The LTI system is causal but not stable. (b) The LTI system is stable but not causal. (c) The LTI system is neither stable nor causal 8...
USE DEFINITION 1 TO DETERMINE THE LAPLACE TRANSFORM OF THE FOLLOWING FUNCTION. f(t)= e sin(t) Laplace Transform Definition 1. Let f(t)be a function on [0,00). The Laplace transform of f is the function defined by the integral The domain of F(s) is all the values of " for which the integral in (1) exists.' The Laplace transform of fis denoted by both and ${/}. QUESTION 2. (3PTS) USE TABLE 7.1 AND 7.2 TO DETERMINE THE LAPLACE TRANSFORM OF THE GIVEN...
Question 9 3 pts The Laplace transform of the piecewise continuous function J4, 0< < 3 f(t) is given by 2, t> 3 2 L{f} (2 - e-st), 8 >0. S L{f} (1 – 3e-), 8>0. 8 2 L{f} (3 - e-s), 8 >0. S L{f} = (1 – 2e-st), s > 0. None of them Question 10 3 pts yll - 4y = 16 cos 2t To find the solution of the Initial-Value Problem y(0) = 0 the y...
Laplace Transform Problem 3. (15 points) Given f(t) = 4e-2tu(t) + 29u(-t) a) Using the Laplace Transform table 9.2 find the bilinear Laplace transform, F($) and sketch the region of convergence (ROC) in the s-plane showing all poles. State the ROC as an inequality. b) Another function is added so that fa(t) = 4e-2tu(t) + 7u(-t) – 10e-10t u(-t). Find the Bilinear Laplace Transform of fa(t) and sketch the region of convergence in s-plane also showing all the poles. State...