1. ## Inverse Laplace Transformation

I have been trying to get my head around this question, but i just can't seem to do it.

Find the Inverse Laplace transform for:

1/s^2(s+1)^2

My steps:
Partial fractions

1/s^2(s+1)^2 = A/s + B/s^2 + C/(s+1) + D/(s+1)^2

Then cross multiplication and collection of like terms

1 = (A+B)(s+1)^2 + C(s+1) +(C+D)s^2 + A(s)

then created 4 equations by substituting the following s values: -1,0,1,2

Then used simultaneous equation solver on my calculator to solve the 4 equations, the calculator shows up with math error.

Where am i going wrong?
Point me in the right direction please.

2. Originally Posted by Kbotz
I have been trying to get my head around this question, but i just can't seem to do it.

Find the Inverse Laplace transform for:

1/s^2(s+1)^2

My steps:
Partial fractions

1/s^2(s+1)^2 = A/s + B/s^2 + C/(s+1) + D/(s+1)^2

Then cross multiplication and collection of like terms

1 = (A+B)(s+1)^2 + C(s+1) +(C+D)s^2 + A(s)

then created 4 equations by substituting the following s values: -1,0,1,2

Then used simultaneous equation solver on my calculator to solve the 4 equations, the calculator shows up with math error.

Where am i going wrong?
Point me in the right direction please.
Your process is correct so your mistake(s) will be in the details (which you have not provided).

3. Oh cool ok
Umm, my 4 equations after the substitution of s = 0,-1,1,2 are:

equation 1 when s = 0

1 = A + B + C

equation 2 when s = -1

1= -A+C+D

equation 3 when s = 1

1 = 5A+4B+3C+D

equation 4 when s =2
1 = 11A + 9B+ 7C + 4D

4. Originally Posted by Kbotz
I have been trying to get my head around this question, but i just can't seem to do it.

Find the Inverse Laplace transform for:

1/s^2(s+1)^2

My steps:
Partial fractions

1/s^2(s+1)^2 = A/s + B/s^2 + C/(s+1) + D/(s+1)^2

Then cross multiplication and collection of like terms

1 = (A+B)(s+1)^2 + C(s+1) +(C+D)s^2 + A(s)

then created 4 equations by substituting the following s values: -1,0,1,2

Then used simultaneous equation solver on my calculator to solve the 4 equations, the calculator shows up with math error.

Where am i going wrong?
Point me in the right direction please.
Putting the right hand side over the common denominator of s^2 (s + 1)^2 and equating numerators on each side, you get:

1 = s(s+1)^2A + (s+1)^2B + (s+1)s^2C + s^2D.

s = 0: 1 = B

s = -1: 1 = D

s = 1: .....

Substitute B = D = 1 to get an equation with A and C.

s = 2: ....

Substitute B = D = 1 to get an equation with A and C.

Solve for A and C simultaneously.

5. it worked!
thank you!