10. Explain using only the Laplace transform formulas developed in class. a) Find the Laplace transform...
Question (2): Laplace Transformsa) Find the Laplace Transform of the following using the Laplace Transform table provided in the back:$$ f(t)=\frac{1}{4}\left(3 e^{-2 t}-8 e^{-4 t}+9 e^{-6 t}\right) u(t) $$b) Find the inverse Laplace Transform \(F(s)\) of the following function \(f(t)\) using the table:$$ f(t)=\frac{12 s^{2}(s+1)}{\left(8 s^{2}+5 s+800\right)(s+5)^{2}(10 s+8)} $$
Find the inverse Laplace transform of the function by using the convolution theorem: 1 F(8) = $3(52 +1)
Use the convolution theorem to find the inverse Laplace transform of the given function. 8 $3 (s2+4) Y-1 8 $3 (s2+4) (t)=
Use the convolution theorem to find the inverse Laplace transform of the given function. 2 s(s? +1) 2 3 (s2 +1)
3 B 1. Find the third roots of 21+ Find the inverse of the Laplace transform 2. tan" G) 3. Check the existence of the Laplace transform for the given function and hence she that -02:49 in 133+ 4 S- where LF(t)) is represent the place transform of (1) [Hint: 2 cos Acos B = (A-2).sin(A+B) + sin(A - m = sin cos sin(A + B) - Sin(A) = 0 4. Find the Fourier Sine series of f(x) <rci 5....
3) al find the Laplace transform F(s) of the function (3-1²"Sebt sin (7+) 6) Find the inverse Laplace transform f(t) of the function F (S) S²+5-20
(1 point) Find the inverse Laplace transform f(t) = C-' {F(s)} of the function F(s) = 2s - 3 32 + 16 560) = c { 2s - 3 32 + 16 = 2cos(4t)-2 sin(4) help (formulas)
(1 point) Find the inverse Laplace transform f(t) = C-' (F(3)) of the function F(s) = 45 52 - 16 f(t) = -1 { 4s s2 - 16 } help (formulas) (6+4+2}- Preview My Answers Submit Answers
(1 point) Find the inverse Laplace transform f(t) = --!{F(s)} of the function 5 9 F(s) = + 52 S+9 S 5 f() = 2-1 { + 640] = s2 help (formulas)
9s 11 (1 pt) Find the inverse Laplace transform f(t) = L=1 {F(s)}| of the function F(s) s2 2s5 9s 11 f(t)= L' help (formulas) $2-2S+5