6. (20 pts) se the definition of convolution to compute tu(t) * u(t); Check your answer...
Problem 4 Given: St t(t) # -t e g(t) a) Compute fg () using convolution integral method. b) Compute g*f () with Laplace transform. o) What are the differences between the results of questions (a) and (0) above? d) Find the Laplace transform of the following function: (t 0 to +oo) e dt e) Find the equivalent solution of (d) using MATLAB method) (find 2 methods) Problem 4 Given: St t(t) # -t e g(t) a) Compute fg () using...
Use the equation below to answer the following question(s) x(t) = cos(a)t)u(t) 4. Using the definition of the Laplace Transform, what is the Laplace Transform of the function above? (Note Y ou must show all work in deriving the transform. You will get no points for picking the correct choice only!) ( +20) c. s2 +203 s2 +23 23
Question 5: (17 points) Use Laplace transform to solve the initial value problem V" - 4y + 4y = 2.814 -- 3)y(0) = 1, (0) = 2 (If you use convolution theorem for an inverse Laplace transform, you need to compute the integral to express your answer explicitly in terms of t.)
0<t<T when Tt< 2 t 2T sin t when 2. Calculate the Laplace transform of the periodic function f(t) 0 f(t-2) when -7s 3. Calculate the inverse Laplace transform of G(s) 3-4e-5 + $2+2s+17 4. Use the Laplace transform to solve each initial value problem: 4y"+ y u2m(t)sin(t/2) y(0)=0 &(0 =0 (a) 0 and /(0) 2 "+4y+13y = 4to(t-T) if y(0) (b) 5. Use the convolution to write a solution of each initial value problem. y"+6y'+10y g(t) 1 y(0) 0...
2(a). Compute and plot the convolution of ytryh)x where h(t) t)-u(t-4), x(t)u(t)-u(t-1) and zero else b). Compute and plot the convolution y(n) h(n)*x (n) where h(n)-1, for 0Sns4, x(n) 1, n 0, 1 and zero else.
1. Solve the ODE/TVP: y" +2y'+y=5(1-2),y(0)-0.7(0) =0. Use the Convolution Theorem everywhere possible, in parts (b) and (c). (a) Find Y(s), the Laplace Transform of y(t), (b) Express y(t) in terms of the convolution product ONLY with explicit functions of t, e.g., f(t)-g(t) or f(t) g(t) * h(t), but do not evaluate any of the convolution product(s); (c) Obtain y(t) by working out completely the convolution product(s) in part (b), show all your intermediate work and results, and simplify your...
6. (a) Determine the inverse Laplace transform of F(8) 2s - 1 32 - 4s +6 (10 marks/ (b) Solve the initial value problem using the method of Laplace transform. 7+10y = 0, y(0) = 0, (0) --3. (20 marks) (c) Solve the initial value problem: 1 dy dy 4 dx2 + 4y = 0, y(0) -- da + (0) = -1 120 marks)
4. (10 points) Use the method of convolution to find (a) (5 points) L-'{[82 +1)62+1)} (b) (5 points) L{f(t)}, where f(t) = S.sin(27) cos(t – )dt 5. (20 points) Using the method of Laplace transform, solve y" – y' – 2y = 0, y(0) = 0, y'(0) = 1,
plz answer both questions, thank you! (1 point) Given that cſ cos(5/6) / e-6.25/s find the Laplace transform of V cos(5vi). {{Vcos(577)} = (1 point) Consider the initial value problem 1" + 4y = cos(2t), y(0) = 3, y(0) = 9. a. Take the Laplace transform of both sides of the given differential equation to create the corresponding algebraic equation. Denote the Laplace transform of y(t) by Y(s). Do not move any terms from one side of the equation to...
(20 pts) 6. Use Laplace Transforms to solve the following I.V.P. 1" + y = 1 - #x/(6) y(0) = 0, 7(0) = 0 Note: The Laplace Transform formulas can be found on the comprehensive table provided on the next page.