# Inverse Laplace Transform of the following fuction

• Mar 12th 2010, 08:05 AM
kaboose786
Inverse Laplace Transform of the following fuction
So the question is: Solve the initial value problem using the method of Laplace transforms:
y'' + 2y' +10y = g(t)
where g(t) = { 10, 0<=t<=10
{ 20, 10<t<20
{ 0, 20< t
so i got it to Y(s) =

http://i40.tinypic.com/66djwn.jpg

now after this if someone can help me take the inverse laplace transform of Y(s) so i can get y(t) ... btw its urgent my hwk is due today :(
• Mar 14th 2010, 12:54 AM
CaptainBlack
Quote:

Originally Posted by kaboose786
So the question is: Solve the initial value problem using the method of Laplace transforms:
y'' + 2y' +10y = g(t)
where g(t) = { 10, 0<=t<=10
{ 20, 10<t<20
{ 0, 20< t
so i got it to Y(s) =

http://i40.tinypic.com/66djwn.jpg

now after this if someone can help me take the inverse laplace transform of Y(s) so i can get y(t) ... btw its urgent my hwk is due today :(

You need to know that:

$\mathcal{L}^{-1} e^{-as}F(s)=f(t-a)u(t-a)$

Then the rest should be doable with partial fractions and table lookup

CB