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Homework Answers
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Problem A Compute the following Laplace Transforms using the definition (not the table): 1. L[10](s) 2....
9.) r-'(2 + - $ }; ; Compute using the table of Laplace Transforms. 1
9.) r-'(2 + - $ }; ; Compute using the table of Laplace Transforms. 1
Detailed answer using the Laplace Transforms method Solve the IVP using the method of Laplace transforms...
Detailed answer using the Laplace Transforms method
Solve the IVP using the method of Laplace transforms AND one other method of your choice. y" +5y' +6y= 2e ; y(0)=1, y'(0) = 3 TABLE 7.2 Properties of Laplace Transforms L{f'}(s) = s£{f}(s) - f(0) L{f"}(s) = s?L{f}(s) – sf(0) – f'(0) . TABLE 71 Brief Table of Laplace Transforms 50 F(x) = ${f}(s) s>0 S 1 => a S a p", n=1,2,... s>0 +1 sin bt s > 0 . s?...
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:$$ f(t)=\frac{12 s^{2}(s+1)}{\left(8 s^{2}+5 s+800\right)(s+5)^{2}(10 s+8)} $$
Match the following Inverse Laplace Transforms with the correct function. 1. L'{c+2} 3tet +tet 2. Li...
Match the following Inverse Laplace Transforms with the correct function. 1. L'{c+2} 3tet +tet 2. Li &e-2443 68 (8-1) et cos(2t) 1 3 ze-3t 31-{s} * L-'{x}2} 5. L- {<2} 2e - 3+ + 2 et
+ 44 7-8 Use the shifting theorems to compute. the inverse Laplace transforms L F (S)...
+ 44 7-8 Use the shifting theorems to compute. the inverse Laplace transforms L F (S) = 25-1 S2-45+20 7. (2 -55 e 8. F(S) = s²+65+10 and lifting theoren
Determine L-'{F} F(s)= -252-6s+2 (s+2)(8+3) Click here to view the table of Laplace transforms. Click here...
Determine L-'{F} F(s)= -252-6s+2 (s+2)(8+3) Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. L-'{f}=0
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)...
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...
8. Using the definition of the Laplace transform compute . {3}(s).
8. Using the definition of the Laplace transform compute . {3}(s).
Express the function below using window and step functions and compute its Laplace transform. Agit) 10...
Express the function below using window and step functions and compute its Laplace transform. Agit) 10 8 10 o 0 2 6 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Express g(t) using window and step functions. Choose the correct answer below. A. g(t) = (4t-8)112,8(t)+(-4+24)ut-4) B. g(t)=ut-2)+(4-8)24t)+(-4+24)114,6(t) +u(t-6) C. g(t)=(4t-2)ut-2)+(-4t+juſt-6) D. g(t)= (4-8)||24t)+(-4+24)11,8(t) Compute the Laplace transform of g(t). L{g}= (Type an expression using s as the...
9.) r-'(2 + - $ }; ; Compute using the table of Laplace Transforms. 1
Detailed answer using the Laplace Transforms method
Solve the IVP using the method of Laplace transforms AND one other method of your choice. y" +5y' +6y= 2e ; y(0)=1, y'(0) = 3 TABLE 7.2 Properties of Laplace Transforms L{f'}(s) = s£{f}(s) - f(0) L{f"}(s) = s?L{f}(s) – sf(0) – f'(0) . TABLE 71 Brief Table of Laplace Transforms 50 F(x) = ${f}(s) s>0 S 1 => a S a p", n=1,2,... s>0 +1 sin bt s > 0 . s?...
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:$$ f(t)=\frac{12 s^{2}(s+1)}{\left(8 s^{2}+5 s+800\right)(s+5)^{2}(10 s+8)} $$
Match the following Inverse Laplace Transforms with the correct function. 1. L'{c+2} 3tet +tet 2. Li &e-2443 68 (8-1) et cos(2t) 1 3 ze-3t 31-{s} * L-'{x}2} 5. L- {<2} 2e - 3+ + 2 et
+ 44 7-8 Use the shifting theorems to compute. the inverse Laplace transforms L F (S) = 25-1 S2-45+20 7. (2 -55 e 8. F(S) = s²+65+10 and lifting theoren
Determine L-'{F} F(s)= -252-6s+2 (s+2)(8+3) Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. L-'{f}=0
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)...
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...
8. Using the definition of the Laplace transform compute . {3}(s).
Express the function below using window and step functions and compute its Laplace transform. Agit) 10 8 10 o 0 2 6 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Express g(t) using window and step functions. Choose the correct answer below. A. g(t) = (4t-8)112,8(t)+(-4+24)ut-4) B. g(t)=ut-2)+(4-8)24t)+(-4+24)114,6(t) +u(t-6) C. g(t)=(4t-2)ut-2)+(-4t+juſt-6) D. g(t)= (4-8)||24t)+(-4+24)11,8(t) Compute the Laplace transform of g(t). L{g}= (Type an expression using s as the...
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