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-...
(1 point) a. Find the Laplace transform F(s)-f(t)) of the function f(t)-7+sin(2t), defined on the interval t 0 F(s) = L(7 + sin(2t)) = help (formulas) b. For what values of s does the Laplace transform exist? help (inequalities)
Apply the Laplace transform to the differential equation, and solve for Y(s) y'25y 2(t 4)u4(t) 2t 8)us(t), y(0) = y'(0) = 0 Y(s) = Preview syntax error Apply the Laplace transform to the differential equation, and solve for Y(s) y'25y 2(t 4)u4(t) 2t 8)us(t), y(0) = y'(0) = 0 Y(s) = Preview syntax error
Use Laplace transform to solve the initial value problem [Answer: У 2tet sin(2t) + 4e* cos(2t) +3t2-21
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)
The Laplace transform of the following time function f (t) = 2t2 + e-2t sin 3t is
10 sin 2t if 0 <t< 4. (a) Let r(t) if t > T Show that the Laplace transform of r(t) is L(r) 20(1 - e - e-78) 32 + 4 (b) Find the inverse Laplace transform of each of the following functions: s – 3 S2 + 2s + 2 20 ii. (52 + 4)(52 + 25 + 2) 20e-S ini. (s2 + 4)(52 + 25 + 2) (c) Solve the following initial value problem for a damped mass-spring...
1. Find the Laplace transform of: f(t) = tet sin 2t u(t)
Question 9 3 pts The Laplace transform of the piecewise continuous function J4, 0< < 3 f(t) is given by 2, t> 3 2 L{f} (2 - e-st), 8 >0. S L{f} (1 – 3e-), 8>0. 8 2 L{f} (3 - e-s), 8 >0. S L{f} = (1 – 2e-st), s > 0. None of them Question 10 3 pts yll - 4y = 16 cos 2t To find the solution of the Initial-Value Problem y(0) = 0 the y...
PROBLEMS Solve for y. 3.1. - x + 4x + sin 6x 3.4. y + 3x = 0 3.5. (x-1)? ydx + x? (y - 1)dy = 0 Just find a solution. Solving for y is tough. Test for exactness and solve if exact. 3.6. (y - x) dx + (x? - y) dy - 0 3.7. (2x + 3y) dx + (3x + y - 1) dy - 0 3.8. (2xy Y + 2xy + y) dx + (x*y*el...
10. Solve the initial value problem using Laplace transforms: y'+6y = 8 sin(2t), y(0) = 2