Verify the following using MATLAB
![2) (a) Consider the following function f(t)=e sinwt u (t (1) .... Write the formula for Laplace transform. L[f)]=F(6) F(6))](http://img.homeworklib.com/questions/080f3c50-135f-11ec-8fcf-993620383634.png?x-oss-process=image/resize,w_560)
![From equation (2), L[eA()]-(+a) L[e sin cot u(t)]= (s+a} +w sin t u(t) Thus, the Laplace transform of e is |(s+a) +w (b) Co](http://img.homeworklib.com/questions/089af740-135f-11ec-b37d-27057e728c93.png?x-oss-process=image/resize,w_560)
![S From equation (4) L[e] (a) wu()]= (s+a) (s+a) coS at (s+a) Therefore, the Laplace transform of e costu(1) 1 s+a} + o is (с)](http://img.homeworklib.com/questions/092e1ed0-135f-11ec-abba-19026a251262.png?x-oss-process=image/resize,w_560)
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Verify the following using MATLAB
2) (a) Consider the following function f(t)=e"" sinwt u (t (1)...
USE DEFINITION 1 TO DETERMINE THE LAPLACE TRANSFORM OF THE FOLLOWING FUNCTION. f(t)= e sin(t) Laplace...
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...
So the time domain for this is v(t) = (1-cos(10pi))[u(t) - u(t-0.1)] + 2[u(t-0.1) - u(t-0.15)] + ...
So the time domain for this is
v(t) = (1-cos(10pi))[u(t) - u(t-0.1)] + 2[u(t-0.1) - u(t-0.15)] +
(-40t+0.2)[u(t-0.15) - u(t-0.25)] + (-2)[u(t-0.25)-u(t-0.3)] +
(2e^(-5(t-0.3)))[u(t-0.3)]
but the equation was reduced before converting into S-domain and
it was reduced to :
v(t) = (-cos(10pi))u(t) + u(t) + cos(10pi)u(t-0.1) + u(t-0.1) -
40(t-0.1))u(t-0.15) + 40(t-0.25)u(t-0.25) + 2u(t-0.3) +
2e^(-5(t-0.3))u(t-0.3)
How do you adjust the time delay? Not sure if I understand how
it was done, if you can show and explain step by...
Find the Laplace transform of each of the following functions. 1. $(t) = f*(4(t – 1)*...
Find the Laplace transform of each of the following functions. 1. $(t) = f*(4(t – 1)* sin(67) dt L{v(t)}(s) = b. g(t) = [ e 2-3(t-1) cos(71) dT L{$(t)}(s) = c. y(t) = e5(t-1) sin(97) cos(6(t – T)) dt L{s(t)}(s) =
Consider the function f(t) whose Laplace transform F(s) = L{f(t)} = $5+2 We know f(0) =...
Consider the function f(t) whose Laplace transform F(s) = L{f(t)} = $5+2 We know f(0) = 0 and f'(0) = 4. Answer the following questions. Please write down the numerators and the denominators separately. Use "A" for the power operation, e.g., write s^5 for 5”. • L{f"(t)}= - Lle="r() = - 19(e) = 'ermite – wsin(26) dw, men zl940)= • If g(t) = wf(t – w)s in (2w) dw, then L{g(t)}= • If y(t) = L-'{e-35F(s)}, then y(1) =D and...
for part A which answer is correct? The given function is... cos(t) f(t) t We know...
for
part A which answer is correct?
The given function is... cos(t) f(t) t We know that the laplace transform of f(t) is given by... Rel(s)> 0 s21 LIf()) Also we know that... f(t) L[ t Lf(lds ds s21 = [In(s2 1) Problem is done cos(t) x(t) t tx(t) cos(t)ut) dX(s) tx(t) ds s2 ds X(s) s2 In(s21) K X(s) = 2 x(t)e dt X(s) -00 X(0) x(t)dt -00 cos(t) dt 0 t -00 K 0 In(s21 X(s) 2 Use...
Determine Laplace Transform of 8(t) = u(t – 2)u(t – 3) [hint: {[u(t)] :)] = :)...
Determine Laplace Transform of 8(t) = u(t – 2)u(t – 3) [hint: {[u(t)] :)] = :) Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
Check the existence of the Laplace transform for the given function and hence show that -...
Check the existence of the Laplace transform for the given function and hence show that - cos 20 1s² + 4 L = In t s2 where L{f(t)} is represent the Laplace transform of f(t). [Hint: 2 cos A cos B = COSIA+B) + cos(A - B) sin(A + B) + sin(A - B) = sinA cosB, sin(A + B) – sin(A - ?) = os AsmB] [2+ Find the Fourier Sine series of [8 f(x) = e-*,0<x<. Using the...
III. When solving this problem show all the steps needed to transform the expressions into ones...
III. When solving this problem show all the steps needed to transform the expressions into ones that can be (10) found in the table and indicate the entry of the table used in each step. a) Find the Laplace transform F(s) of the function (5+234 +5e-2) cos(6t) b) Find the inverse Laplace transform f(t) of the function F(s) = 2 s2 + 2s + 5 f(t)=L-'{F(s) Table of Laplace Transforms F(s)=L{()} f(t)= L-'{F(s) F(s)=L{f(t)} 1. 2. et s-a 3. r",...
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) =...
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) = x(s)H(s). Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
e Let f(t) be a function on [0, 0). The Laplace transform off is the function...
e Let f(t) be a function on [0, 0). The Laplace transform off is the function F defined by the integral F(s) = s e -stf(t)dt. Use this definition to determine the Laplace transform of the following function. 0 0<t<3 f(t)= 4, 3<t e 6-35 s-1 4 The Laplace transform of f(t) is F(s) = + e - 3s for all positive s# 2 and F(s) = 3+2 e -6 2-S S otherwise. (Type exact answers.)
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...
So the time domain for this is
v(t) = (1-cos(10pi))[u(t) - u(t-0.1)] + 2[u(t-0.1) - u(t-0.15)] +
(-40t+0.2)[u(t-0.15) - u(t-0.25)] + (-2)[u(t-0.25)-u(t-0.3)] +
(2e^(-5(t-0.3)))[u(t-0.3)]
but the equation was reduced before converting into S-domain and
it was reduced to :
v(t) = (-cos(10pi))u(t) + u(t) + cos(10pi)u(t-0.1) + u(t-0.1) -
40(t-0.1))u(t-0.15) + 40(t-0.25)u(t-0.25) + 2u(t-0.3) +
2e^(-5(t-0.3))u(t-0.3)
How do you adjust the time delay? Not sure if I understand how
it was done, if you can show and explain step by...
Find the Laplace transform of each of the following functions. 1. $(t) = f*(4(t – 1)* sin(67) dt L{v(t)}(s) = b. g(t) = [ e 2-3(t-1) cos(71) dT L{$(t)}(s) = c. y(t) = e5(t-1) sin(97) cos(6(t – T)) dt L{s(t)}(s) =
Consider the function f(t) whose Laplace transform F(s) = L{f(t)} = $5+2 We know f(0) = 0 and f'(0) = 4. Answer the following questions. Please write down the numerators and the denominators separately. Use "A" for the power operation, e.g., write s^5 for 5”. • L{f"(t)}= - Lle="r() = - 19(e) = 'ermite – wsin(26) dw, men zl940)= • If g(t) = wf(t – w)s in (2w) dw, then L{g(t)}= • If y(t) = L-'{e-35F(s)}, then y(1) =D and...
for
part A which answer is correct?
The given function is... cos(t) f(t) t We know that the laplace transform of f(t) is given by... Rel(s)> 0 s21 LIf()) Also we know that... f(t) L[ t Lf(lds ds s21 = [In(s2 1) Problem is done cos(t) x(t) t tx(t) cos(t)ut) dX(s) tx(t) ds s2 ds X(s) s2 In(s21) K X(s) = 2 x(t)e dt X(s) -00 X(0) x(t)dt -00 cos(t) dt 0 t -00 K 0 In(s21 X(s) 2 Use...
Determine Laplace Transform of 8(t) = u(t – 2)u(t – 3) [hint: {[u(t)] :)] = :) Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
Check the existence of the Laplace transform for the given function and hence show that - cos 20 1s² + 4 L = In t s2 where L{f(t)} is represent the Laplace transform of f(t). [Hint: 2 cos A cos B = COSIA+B) + cos(A - B) sin(A + B) + sin(A - B) = sinA cosB, sin(A + B) – sin(A - ?) = os AsmB] [2+ Find the Fourier Sine series of [8 f(x) = e-*,0<x<. Using the...
III. When solving this problem show all the steps needed to transform the expressions into ones that can be (10) found in the table and indicate the entry of the table used in each step. a) Find the Laplace transform F(s) of the function (5+234 +5e-2) cos(6t) b) Find the inverse Laplace transform f(t) of the function F(s) = 2 s2 + 2s + 5 f(t)=L-'{F(s) Table of Laplace Transforms F(s)=L{()} f(t)= L-'{F(s) F(s)=L{f(t)} 1. 2. et s-a 3. r",...
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: L[x(t)h(t)) = x(s)H(s). Useful Formula: Fourier Transform: F[f(t)] = F(w) sof(t)e-jw dt Inverse Fourier Transform: F-1[F(w)] = f (t) = 24., F(w)ejwidw Time Transformation property of Fourier Transform: f(at – to). FC)e=itoch Laplace Transform: L[f(t)] = F(s) = $© f(t)e-st dt Shifting property: L[f(t – to)u(t – to)] = e-toSF(s) e [tuce) = 1 and c [u(e) = )
e Let f(t) be a function on [0, 0). The Laplace transform off is the function F defined by the integral F(s) = s e -stf(t)dt. Use this definition to determine the Laplace transform of the following function. 0 0<t<3 f(t)= 4, 3<t e 6-35 s-1 4 The Laplace transform of f(t) is F(s) = + e - 3s for all positive s# 2 and F(s) = 3+2 e -6 2-S S otherwise. (Type exact answers.)
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