- #1
Twinflower
- 109
- 0
Homework Statement
[tex]I(s)=\frac{2}{s^2 + s}[/tex]
Convert this to the time domain
The Attempt at a Solution
Step 1 - Divide by s
[tex]I(s)=\frac{\frac{2}{s}}{s + 1}[/tex]
Step 2 - Substract and add 1 to create new fractions
[tex]I(s)=\frac{\frac{2}{s}-1+1}{s + 1}[/tex]
Step 3 - Split into new fractions
[tex]I(s)=\frac{\frac{2}{s}}{s + 1} - \frac{1}{s + 1} + \frac{1}{s + 1}[/tex]
Step 4 - Contract the two newbie fractions
[tex]I(s)=\frac{\frac{2}{s}}{s + 1} - \frac{2}{s + 1}[/tex]
Step 5: Split up the first fraction
[tex]I(s)=\frac{2}{s} \frac{1}{s + 1} - \frac{2}{s + 1}[/tex]
Step 6 - Convert to time domain
[tex]i(t)=2e^{-t}-e^{-t}[/tex]
BUT, this is not correct. It should be: [itex] 2-2e^{-t}[/itex]
What is wrong in my approach here?