Find the Laplace transform of the function f(t). f(t) = sint if o St<$21; f(t) = 0 if t> 21 Click the icon to view a short table of Laplace transforms. F(S) =
Find the Laplace transform of the function f(t). f(t) = sint if 0 St< $41; f(t) = 0 ift> 41 Click the icon to view a short table of Laplace transforms. F(s)=
10:53 homework7 11 Homework7: Problem 11 Previous Problem List Next (1 point) Consider the function if0<t<2 a. Use the graph of this function to write it in terms of the Heaviside function. Use h(t - a for the Heaviside function shifted a units horizontally f(t) help (formulas) b. Find the Laplace transform 0. F(s) = L U(t)) for s help (formulas) Note: You can earn partial credit on this problemm. Pr
4. Find the Laplace transform of the following function. 0 st<1 t + 1 1s1<2 g(t) = 2st<3 01
piny 1520 7e ECW-3: Problem 16 Previous Problem List Next (1 point) The graph of f(t) is given below a. Represent f) using a combination of Heaviside step functions. Use ht - a) for the Heaviside function shifted a units horizontally f(t) = help (formulas) . Find the Laplace transform F(8) = C{f(0)} for 8 +0. F(s) = C {f(t)} = help (formulas) Note: You can earn partial credit on this problem
(1 point) Given the function f(t) = {sine if 0 <t< 61 if 61 <t. sint 61) Express f(t) in terms of the shifted unit step function uſt – a) f(t) = Now find the Laplace transform F(s) of f(t) F(s) =
2. Let t if 5 < t < 10 f(t) = -{ e3t if t > 10 Use the Heaviside step function to evaluate the Laplace of f. (4 pts.) 3. Find the inverse Laplace transform of the following functions: (i) F(s) = 4s +5 s(s2 + 4s + 5) (3 pts.) -35 (ii) G(s) = 4s + 5 s(s2 + 4s + 5) е (you may use part (i)) (2 pts.)
(4) Find the Laplace transform of this function: Set if 0 <t <2, 0 if 2 <t.
10. Use the Laplace transform to solve y" - 3y' +2y f(t), y(0)-0,'(0) 0, where (t)-(0 for 0 st < 4; for t 2 4 No credit will be given for any other method. (10 marks)
Answer all the problems please. (1 point) The graph of f(t) is given below (Click on graph to enlarge) a. Represent f(t) using a combination of Heaviside step functions. Use h(t - a) for the Heaviside function shifted a units horizontally f(t) = help (formulas) b. Find the Laplace transform F(s) = L {f(t)) for s 0. F(s) = L {f(t)) = help (formulas) (1 point) Find the inverse Laplace transform of 7s F(s) = s2-15-12 f(t)-H(t-7)*(1/7% . (Use step(t-c)...