Evaluate the Laplace Transform: L{ t4et} O 24 (8-1)5 None of them 6 (s-1) . 1...
Determine Laplace transform of L{t sin3t}. O S $2 +9 O 6s (52 +9) None of them o S (52 +9) 2s (3² + 3)²
Determine Laplace Transform of f(t) = 2sin3t + 4t? OF(8) 6 + 24 82 +9 24 84 OF(S) 3 - + $2 +9 84 None of them 0 F (s) = 27, +42
6 (1 Point) 1 Let L{sint} 5* +1 Laplace transform of tant and L{cost}= 3 -1 What is the a) ? b)s c) not defined d) None of these S a b U c d
Please show work! (1 point) Find the Laplace transform F(s) of f(t) { O, t<6 5 sin(at), 6<t<7 0, t> 7 F(8)
Use Laplace Transform to identify Y(s) of the DE: y"-y'-by = 0, given y(0) = 1, y'(O) = 2. O None of them Both are correct. Y(s) = 4 5(8-3) + 5(8+2) OY (s) = 8+1 (5-3)(8+2)
Show your complete work. 10 points. The Laplace transform of the piece wise continuous o<t<3 is given by: a) None of them 6) L {f} = = (2-e-st), S70 c)L{f} = 2 (3-e-st), s so dX[f) = 4 (1-2 est), so e) L {f} = } Show your complete wone. = ₃ (1-3e-st), 530
(write fraction as After use Laplace Transform to transform the following initial value problem rret, x(O)= 1,x'(0)=1, you should get X(s)= S-2 (S-2)/(5-4)(8+6) for -). Then, find x(t) = L-?{x(s)}= (s – 4)(s+6) 5 -3t (write 5/6 by 6' , e^{-3t} by e and sin(2t) or cos(3t) by sin(2t) or cos(3t)).
Find the Inverse Transform L {F(s)} of F(s) 38+2 $2 -38 +2 o L 1{F(s)} = 8e2t - 5et OL-'{F(s)} 5 8-1 $ 2 L'{F(s)} = -5e2-8et None of them
Find the Laplace transform of e' sin(t). none of these s+1 2?+(3+1) s+1 q?+(3+1) a 22+(+1) O a c? +(5-1)
Find the Laplace transform Y (8) = L {y} of the solution of the given initial value problem. y" + 16y S 1, 0 <t<T , YO) = 5, y' (0) = 9 0, <t<oo Enclose numerators and denominators in parentheses. For example, (a - b)/(1+n). Y (8) = Qe