B.) Utilize Laplace transform to compute the u(x,t): Limit
B.) Utilize Laplace transform to compute the u(x,t):
Limit 
Homework Answers
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Determine the Laplace transform of x(t) = t2 u(t – 1) (b) Use Laplace transform to...
Determine the Laplace transform of x(t) = t2 u(t – 1) (b) Use Laplace transform to solve the following differential equation for t ≥ 0. ? 2?(?) ?? 2 + 3 ??(?) ?? + 2?(?) = (? −? ????)?(?); ?(0) = 1; ??(0) ?? = −3
2. Solve for u(x,t) using Laplace transform (13.5.5) a(x,0) /ar f(x). =
2. Solve for u(x,t) using Laplace transform (13.5.5) a(x,0) /ar f(x). =
2. Solve for u(x,t) using Laplace transform (13.5.5) a(x,0) /ar f(x). =
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) = )
1. Obtain Laplace transform of the following functions using the Laplace transform definition a. x(t)-sin!) b....
1. Obtain Laplace transform of the following functions using the Laplace transform definition a. x(t)-sin!) b. x(t)-t
Compute the Laplace transform of the function on [0, oo). Here, uc (t)ut c where u(t)...
Compute the Laplace transform of the function on [0, oo). Here, uc (t)ut c where u(t) is the Heaviside function on [0, oo). Give your answer as a function of 8 for 8 〉 0. (f)(s) =
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) = )
18. Given f(t) = e-at sin(bt) u(t) Using the Laplace transform properties find the Laplace transform...
18. Given f(t) = e-at sin(bt) u(t) Using the Laplace transform properties find the Laplace transform of a) g(t) = tf(t) b) m(t) = f(t - 3) this means replace all the occurrences of t with t-3 in f(t)
18. Given f(t) = e-at sin(bt) u(t) Using the Laplace transform properties find the Laplace transform...
18. Given f(t) = e-at sin(bt) u(t) Using the Laplace transform properties find the Laplace transform of a) g(t) = tf(t) b) m(t) = f(t - 3) this means replace all the occurrences of t with t-3 in f(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: [[x(+) *...
Determine the system response y(t) for h(t)=u(t)+u(t-2) and x(t)=u(t). [Hint: use Laplace Transform multiplication: [[x(+) * h(t)] = X(s)H(s).] y(t) = tu(t)-(t - 2)u(t-2) y(t) = tu(t)+(t-2)u(t-2) y(t) = tu(t)-(t +2)u(t+2) y(t) = tu(t) + (t-2)u(t+2)
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10-...
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10- O A. g(t) = u(t-1)+(77-7)111,2(t) +(-7t+21)112,3(t) + u(t - 3) B. g(t) = (7t - 7)111,2(t) +(-7t+21)112,3(t) C. g(t) = (77–7)114,3(t) +(-7t+21)u(t-2) Click to select your answer(s). x Ag(t) 1044 0+ 0 2 4 6 00- 10 OK Compute the Laplace transform of g(t). L{g} = (Type an expression using s as the variable.) Click to select your answer(s).
2. Solve for u(x,t) using Laplace transform (13.5.5) a(x,0) /ar f(x). =
2. Solve for u(x,t) using Laplace transform (13.5.5) a(x,0) /ar f(x). =
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) = )
1. Obtain Laplace transform of the following functions using the Laplace transform definition a. x(t)-sin!) b. x(t)-t
Compute the Laplace transform of the function on [0, oo). Here, uc (t)ut c where u(t) is the Heaviside function on [0, oo). Give your answer as a function of 8 for 8 〉 0. (f)(s) =
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) = )
18. Given f(t) = e-at sin(bt) u(t) Using the Laplace transform properties find the Laplace transform of a) g(t) = tf(t) b) m(t) = f(t - 3) this means replace all the occurrences of t with t-3 in f(t)
18. Given f(t) = e-at sin(bt) u(t) Using the Laplace transform properties find the Laplace transform of a) g(t) = tf(t) b) m(t) = f(t - 3) this means replace all the occurrences of t with t-3 in f(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: [[x(+) * h(t)] = X(s)H(s).] y(t) = tu(t)-(t - 2)u(t-2) y(t) = tu(t)+(t-2)u(t-2) y(t) = tu(t)-(t +2)u(t+2) y(t) = tu(t) + (t-2)u(t+2)
Express the function below using window and step functions and compute its Laplace transform. Ag(t) 10- O A. g(t) = u(t-1)+(77-7)111,2(t) +(-7t+21)112,3(t) + u(t - 3) B. g(t) = (7t - 7)111,2(t) +(-7t+21)112,3(t) C. g(t) = (77–7)114,3(t) +(-7t+21)u(t-2) Click to select your answer(s). x Ag(t) 1044 0+ 0 2 4 6 00- 10 OK Compute the Laplace transform of g(t). L{g} = (Type an expression using s as the variable.) Click to select your answer(s).
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