5s? +8s +2 (10 points: 5+5) Consider a function: F(s) = 2. 2s° + 2s +s...
s2+15 X(s) (s2+5s+ 6) (s2 +9) Find: (a) Use Partial Fractions Decomposition to write the rational function as the sum of simpler expressions (b) Obtain the time-domain solution, x(t), by finding the inverse Laplace Transform of X(s) f(t)) had initial conditions, x(0) 0 and (c) Consider the inverse question, if the ODE (ä + ax + bx = 1, what was the input function in the time domain, f(t) (0) s2+15 X(s) (s2+5s+ 6) (s2 +9) Find: (a) Use Partial...
Determine the inverse Laplace transform of the function below. Se - 2s S2 + 8s +32 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. - 2s Se - 1 >(t) = $2 +85 +32 (Use parentheses to clearly denote the argument of each function.)
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) =...
Determine the inverse Laplace transform of the function below. 5s Se s? + 85 + 25 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. - 5s se 8-1 >(t) = 2 S' + 8s + 25 (Use parentheses to clearly denote the argument of each function.)
5s2 +5s + 12 (1 point) Consider the function F(s) - a. Find the partial fraction decomposition of F(s): 5s2 +5s + 12 b. Find the inverse Laplace transform of F f(t) = C-1 {F(s)) = help (foi
7 11. If a particular network is described by transfer function H(s), use MATLAB to plot the magnitude and phase Bode plot for H(s) equal to (a) 300 (s2 7s +7 s(5s +8s(2s + 4) 7 11. If a particular network is described by transfer function H(s), use MATLAB to plot the magnitude and phase Bode plot for H(s) equal to (a) 300 (s2 7s +7 s(5s +8s(2s + 4)
Applied Mathematics Laplace Transforms 1. Consider a smooth function f(t) defined on 0 t<o, with Laplace transform F(s) (a) Prove the First Shift Theorem, which states that Lfeatf(t)) = F(s-a), where a is a constant. Use the First Shift Theorem to find the inverse trans- form of s2 -6s 12 6 marks (b) Prove the Second Shift Theorem, which states that L{f(t-a)H(t-a))-e-as F(s), where H is the Heaviside step function and a is a positive constant. Use the First and...
(1 point) Consider the initial value problem d2y dy 8 +41y8 cos(2t), dt dy (0) y(0) = -2 -6 dt dt2 Write down the Laplace transform of the left-hand side of the equation given the initial conditions (sA2-8s+41)Y+2s-18 Your answer should be a function of s and Y with Y denoting the Laplace transform of the solution y. Write down the Laplace transform of the right-hand side of the equation (-8s+32)/(sA2-8s+20) Your answer should be a function of s only...
Find the inverse Laplace transform of the function F(s) s +1 $2 - 8s + 20 * uz(t)e(4t-12) (cos(2t – 6) + 2.5 sin(2t – 6)) OF U3(t)e4t (cos(2t – 3) + 0.5 sin(2t – 3)) OC e(4t-12) (cos(2t – 3) + sin(2t – 3)) OD uz(t) (cos(2t – 6) + sin(2t – 6)) ОЕ uz(t) (e4t – 5t)
· Evaluate the following inverse Laplace transform 2-1 S 5s + 3 ) 1 s2 + 4s +5% ] Solve the following system of differential equations S x' – 4x + y" | x' + x + y = 0, = 0. Use the method of Laplace Transforms to solve the following IVP y" + y = f(t), y(0) = 1, y'(0) = 1, where f(t) is given by J21 0, t>1. f(t) = {t, Ost<1, PIC.COLLAGE