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9-8 Find the Laplace transform of f(t)=54cos(100 3sin(10t)] u(t). Locate the poles and zeros of F(s).
1) Laplace transforms/Transfer functions Use Laplace transform tables!!!! 1.1: Find the Laplace transform of - 4t) f(t) = lc + e *).u(t) (simplify into one ratio) 1.2.. Find the poles and zeros of the following functions. Indicate any repearted poles and complex conjugate poles. Expand the transforms using partial fraction expansion. 20 1.2.1: F(s) = (s + 3).(52 + 8 + 25) 1.2.2: 252 + 18s + 12 F(s) =- 54 + 9.5? + 34.5² + 90-s + 100
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...
I need help with these Laplace problems:) (1 point) Find the Laplace transform of <9 f(t) = { 0, " I(t - 9)?, 129 F(s) = (1 point) Find the inverse Laplace transform of e-75 F(s) = 52 – 2s – 15 f(t) = . (Use step(t-c) for uc(t).) (1 point) Find the Laplace transform of 0. f(t) t<5 112 – 10t + 30, 125 F(s) =
Find Laplace Transform Find the Laplace transform F(s) = ({f(t)} of the function f(t) = 4 + 4 + sin(8t). F(s) = ({4+4+" + sin(8t)} =
16. Given f(t) = 2e-tu(t) + 4u(-t) a) Using the Unilateral Laplace Transform table and the procedure described in class and the text, determine the Bilinear Laplace Transform Fb (s) and sketch the region of convergence (ROC) in the s-plane showing poles. State the ROC as an inequality. b) Another function is added so that fa(t) = 2e-u(t) + 4u(-t) + 4e -0.5t u(t). Find the Bilinear Laplace Transform and sketch the region of convergence in s-plane also showing poles.
Find the Laplace transform of f(t)=∫ 0 t τsin(2τ) dτ F(s)= Find the Laplace transform of f(t) = Tsin(27) dt F() =
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) = )
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:$$ f(t)=\frac{12 s^{2}(s+1)}{\left(8 s^{2}+5 s+800\right)(s+5)^{2}(10 s+8)} $$
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)