What Steps Are Involved in Solving Complex Inverse Laplace Transforms?

[guava91011]

Homework Statement

Hi all,

I'm struggling to find the Inverse Laplace transform of the following function:

F(s) = (1+ 4e(-s) - 5e(-3s)) / s(s2 + 11s + 55), where F(s) is a Laplace transform

Solution should be in terms of complex exponentials and unit step functions.

Homework Equations

The Attempt at a Solution

After attempting I got a solution in terms of complex co-efficients, complex exponential functions and heaviside step functions. A part of my solution is:

(1/55) - (3 - i*sqrt(11))/330*exp(*-0.5(11 - 3i*sqrt(11))*t) - ...
-(2(3 - i*sqrt(11))/165)*exp(0.5(11 + 3i*sqrt(11))*(1-t))*u(t-1)...

 

[guava91011]

Anyone have an idea?

 

[Ray Vickson]

Homework Statement

Hi all,

I'm struggling to find the Inverse Laplace transform of the following function:

F(s) = (1+ 4e(-s) - 5e(-3s)) / s(s2 + 11s + 55), where F(s) is a Laplace transform

Solution should be in terms of complex exponentials and unit step functions.

Homework Equations

The Attempt at a Solution

After attempting I got a solution in terms of complex co-efficients, complex exponential functions and heaviside step functions. A part of my solution is:

(1/55) - (3 - i*sqrt(11))/330*exp(*-0.5(11 - 3i*sqrt(11))*t) - ...
-(2(3 - i*sqrt(11))/165)*exp(0.5(11 + 3i*sqrt(11))*(1-t))*u(t-1)...

Can you find G(t), the inverse Laplace of g(s) = 1/D(s), where D(s) = s*(s^2 + 11s + 55)? Do you know how to find the inverse Laplace transform of h(s) = exp(-as)/g(s) in terms of the function G(.)? (Hint: think standard properties of Laplace transforms; use Google if needed.)

RGV