Homework Answers
![Az = 205 B - - 2.5 T=5] so y(s) = 2-5 -2.5 + 5 (5+3) (sto (571)2 taking inverge laplace transform. * y (t) = [2.583t 250 * +5](http://img.homeworklib.com/questions/662b9dc0-155b-11ec-b966-0de70a036b44.png?x-oss-process=image/resize,w_560)
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Derive time-domain function y(t) of the following Laplace transforms. 10 (s+1)2(5+3) (a) Y(s) = (5+1)+(5+3) (b)...
3. Let the Laplace transforms of signals (t) and y(t) be X(s) and Y(s) with appropriate...
3. Let the Laplace transforms of signals (t) and y(t) be X(s) and Y(s) with appropriate regions of convergence, respectively (a) Show that the Laplace transform of x(t) * y(t) is X(s)Y (s). What is the region of convergence? (b) Show that the Laplace transform of tx(t) is -dX(s)/ds with the same region of x(t) convergence as tn-1 1 for Re{sa} > 0. -at e (c) Show that the Laplace transform of 'u(t) is n 1)! (sa)" 1 for Refsa}...
Find the inverse Laplace transforms of (a) (b) (c) s 1 (2s +1) Y(s) = (822 5s + 8 (2s - 2) 21) Y(s) = Find the inverse Laplace transforms of (2s- 3)e-3,s 1) (2s (a) Y(s)2s+ ) (2s - 2) (c) Y(s)...
Find the inverse Laplace transforms of
(a)
(b)
(c)
s 1 (2s +1) Y(s) = (822 5s + 8 (2s - 2) 21) Y(s) = Find the inverse Laplace transforms of (2s- 3)e-3,s 1) (2s (a) Y(s)2s+ ) (2s - 2) (c) Y(s) = (5-7)2
s 1 (2s +1)
Y(s) = (822 5s + 8 (2s - 2)
21) Y(s) =
Find the inverse Laplace transforms of (2s- 3)e-3,s 1) (2s (a) Y(s)2s+ ) (2s - 2) (c) Y(s) =...
Compute Laplace transforms of the following functions: (a) f1 = (1 + t) (b) f2 =...
Compute Laplace transforms of the following functions: (a) f1 = (1 + t) (b) f2 = eat sin(bt) 11, 0<t<1, (c) f3 = -1 1<t<2, | 2, t>2, Find the functions from their Laplace transforms: (a) Lyı] s(s + 1) (s +3) 2+s (b) L[42] = 52 + 2 s +5 (c) L[y3] = Solve the following initial value problems using the Laplace transform. Confirm each solution with a Matlab plot showing the function on the interval 0 <t<5. (a)...
1 +s Find the inverse Laplace transforms of the following: a. F(s) = a (s+2)2 b....
1 +s Find the inverse Laplace transforms of the following: a. F(s) = a (s+2)2 b. F(s) = -25- Hint: Complete the square in denominator 2s -1 s2-2s +10
Question (2): Laplace Transforms a) Find the Laplace Transform of the following using the Laplace Transform...
Question (2): Laplace Transformsa) Find the Laplace Transform of the following using the Laplace Transform table provided in the back:$$ f(t)=\frac{1}{4}\left(3 e^{-2 t}-8 e^{-4 t}+9 e^{-6 t}\right) u(t) $$b) Find the inverse Laplace Transform \(F(s)\) of the following function \(f(t)\) using the table:$$ f(t)=\frac{12 s^{2}(s+1)}{\left(8 s^{2}+5 s+800\right)(s+5)^{2}(10 s+8)} $$
Homework Set 5 f(t) F(S) Section 4.1: Apply the definition to directly find the Laplace transforms...
Homework Set 5 f(t) F(S) Section 4.1: Apply the definition to directly find the Laplace transforms of the given functions. (s > 0) 1 (s > 0) S- 1. Kt) = 12 2. f = 23t+1 Use transforms from the Table (op right) to find the Laplace transforms of the given functions. t" ( n20) (s > 0) r(a + 1) 1a (a > -1) (s > 0) 5+1 3. f(t) = VE +8t 4. f(t) = sin(2tcos(2t) Use the...
Purpose: Use Laplace transforms to find the time domain response of a RLC band-pass filter to...
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...
Find the time domain equations for the following frequency domain equation by using inverse Laplace transformation....
Find the time domain equations for the following frequency domain equation by using inverse Laplace transformation. 52 +55+6 (s+4)(s+1) 8(s+1)(s+3) s(s+2)(s+4) (3) 552 +7s+29 s(s2 +45+29) s(s+4)(s2 +65 +10)
(6 points): Find the time function corresponding to each of the following Laplace transforms: (a) f(t)=3(SIFT)...
(6 points): Find the time function corresponding to each of the following Laplace transforms: (a) f(t)=3(SIFT) (b) f(t)=(a+1)(s26s+610) (c) f(t) =(612(st2)16) (c) f(t) = (HI52 16)
y(t)=? Solve the following differential equation by Laplace transforms. The function is subject to the given...
y(t)=?
Solve the following differential equation by Laplace transforms. The function is subject to the given conditions. y'' +81y = 0, y(0) = 0, y'(0) = 1 Click the icon to view the table of Laplace transforms. y = (Type an expression using t as the variable. Type an exact answer.)
3. Let the Laplace transforms of signals (t) and y(t) be X(s) and Y(s) with appropriate regions of convergence, respectively (a) Show that the Laplace transform of x(t) * y(t) is X(s)Y (s). What is the region of convergence? (b) Show that the Laplace transform of tx(t) is -dX(s)/ds with the same region of x(t) convergence as tn-1 1 for Re{sa} > 0. -at e (c) Show that the Laplace transform of 'u(t) is n 1)! (sa)" 1 for Refsa}...
Find the inverse Laplace transforms of
(a)
(b)
(c)
s 1 (2s +1) Y(s) = (822 5s + 8 (2s - 2) 21) Y(s) = Find the inverse Laplace transforms of (2s- 3)e-3,s 1) (2s (a) Y(s)2s+ ) (2s - 2) (c) Y(s) = (5-7)2
s 1 (2s +1)
Y(s) = (822 5s + 8 (2s - 2)
21) Y(s) =
Find the inverse Laplace transforms of (2s- 3)e-3,s 1) (2s (a) Y(s)2s+ ) (2s - 2) (c) Y(s) =...
Compute Laplace transforms of the following functions: (a) f1 = (1 + t) (b) f2 = eat sin(bt) 11, 0<t<1, (c) f3 = -1 1<t<2, | 2, t>2, Find the functions from their Laplace transforms: (a) Lyı] s(s + 1) (s +3) 2+s (b) L[42] = 52 + 2 s +5 (c) L[y3] = Solve the following initial value problems using the Laplace transform. Confirm each solution with a Matlab plot showing the function on the interval 0 <t<5. (a)...
1 +s Find the inverse Laplace transforms of the following: a. F(s) = a (s+2)2 b. F(s) = -25- Hint: Complete the square in denominator 2s -1 s2-2s +10
Question (2): Laplace Transformsa) Find the Laplace Transform of the following using the Laplace Transform table provided in the back:$$ f(t)=\frac{1}{4}\left(3 e^{-2 t}-8 e^{-4 t}+9 e^{-6 t}\right) u(t) $$b) Find the inverse Laplace Transform \(F(s)\) of the following function \(f(t)\) using the table:$$ f(t)=\frac{12 s^{2}(s+1)}{\left(8 s^{2}+5 s+800\right)(s+5)^{2}(10 s+8)} $$
Homework Set 5 f(t) F(S) Section 4.1: Apply the definition to directly find the Laplace transforms of the given functions. (s > 0) 1 (s > 0) S- 1. Kt) = 12 2. f = 23t+1 Use transforms from the Table (op right) to find the Laplace transforms of the given functions. t" ( n20) (s > 0) r(a + 1) 1a (a > -1) (s > 0) 5+1 3. f(t) = VE +8t 4. f(t) = sin(2tcos(2t) Use the...
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...
Find the time domain equations for the following frequency domain equation by using inverse Laplace transformation. 52 +55+6 (s+4)(s+1) 8(s+1)(s+3) s(s+2)(s+4) (3) 552 +7s+29 s(s2 +45+29) s(s+4)(s2 +65 +10)
(6 points): Find the time function corresponding to each of the following Laplace transforms: (a) f(t)=3(SIFT) (b) f(t)=(a+1)(s26s+610) (c) f(t) =(612(st2)16) (c) f(t) = (HI52 16)
y(t)=?
Solve the following differential equation by Laplace transforms. The function is subject to the given conditions. y'' +81y = 0, y(0) = 0, y'(0) = 1 Click the icon to view the table of Laplace transforms. y = (Type an expression using t as the variable. Type an exact answer.)
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