Laplace Inverse Problems: 1/(s^2-6s+10) and s/(s+1)^2 Solutions

[bdh2991]

Homework Statement

I have two problems i can't figure out , laplace inverse of 1/(s^2-6s+10) and laplace inverse of s/(s+1)^2

Homework Equations

I use the table of laplace transforms in my book

The Attempt at a Solution

For the first one i did the quadratic formula to solve for s but i still couldn't figure out the answeer

And the second one i split up the denominator and was thinkin a=-1 and b=-1 but i didnt get the right answer...im really having a hard timewith this stuff i feel like I am making it harder than it really is please help

 

[Mark44]

Homework Statement

I have two problems i can't figure out , laplace inverse of 1/(s^2-6s+10) and laplace inverse of s/(s+1)^2

Homework Equations

I use the table of laplace transforms in my book

The Attempt at a Solution

For the first one i did the quadratic formula to solve for s but i still couldn't figure out the answeer

And the second one i split up the denominator and was thinkin a=-1 and b=-1 but i didnt get the right answer...im really having a hard timewith this stuff i feel like I am making it harder than it really is please help

For the first, 1/(s^2-6s+10) = 1/( (s - 3)² + 1). You can think of this as F(s - 3), where F(s) = 1/(s² + 1). I think this is the direction you should take, but I haven't worked this one through.

For the second one, I don't think you set up your partial fraction decomposition correctly. If you wrote it as
$$\frac{s}{(s + 1)^2} = \frac{A}{s+1} + \frac{B}{s+1}$$

that is incorrect.
It should be

$$\frac{s}{(s + 1)^2} = \frac{A}{s+1} + \frac{B}{(s+1)^2}$$

 

[bdh2991]

ya i realized the first one you have to complete the square but for i haven't reworked the second one i'll try the partial fractions and see if it works out...thanks for the help!