Compute the inverse Laplace transform of F(s) using the convolution theo- rem. You may leave your...
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. 4 s' (s2 + 4) **** 14.30-0 $(2+4)
Use the convolution theorem to find the inverse Laplace transform of the given function. 2 s(s? +1) 2 3 (s2 +1)
(15 points) Use the convolution theorem to find the inverse Laplace transform f(t) of F(s) = 32 2 $'(92 + 4) f(t) = 16sin^2(t)
10. Explain using only the Laplace transform formulas developed in class. a) Find the Laplace transform of uſt - 3) sin (htt) b) Find the inverse Laplace transform of the function using convolution F(s)G(s) = f(t) *g(t) 1 s? (s2 + 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)=
3. Find the inverse Laplace transform of F(s)-
3. Find the inverse Laplace transform of F(s)-
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.)
Solve the following IVP using the Laplace Transform. Do not leave your answer in terms of an integral. y" - y = -k8(t – 4), y(0) = 3, y'(0) = 3, kER, > 0
Use the convolution theorem to find the inverse Laplace transform of the given function. 2 $3 (s2+4) 2 >(t)= (s2+4) s3