Please point out any mistakes in the solution

[PA3040D]

Dear expert, I would greatly appreciate it if someone could review the following question and answer. Please point out any errors in the answer, and let me know if there are any mistakes in my approach to solving the question. Thank you."

 

[mario99]

Everything was good until this step:

$\displaystyle \mathcal{L}^{-1}\left\{\frac{s}{\left(s + \frac{1}{2}\right)^2+\left(\frac{\sqrt{3}}{2}\right)^2}\right\}$

If you will add $\displaystyle \frac{1}{2}$ you should also subtract $\displaystyle \frac{1}{2}$, like this:

$\displaystyle \mathcal{L}^{-1}\left\{\frac{s + \frac{1}{2} - \frac{1}{2}}{\left(s + \frac{1}{2}\right)^2+\left(\frac{\sqrt{3}}{2}\right)^2}\right\} = \mathcal{L}^{-1}\left\{\frac{s + \frac{1}{2} }{\left(s + \frac{1}{2}\right)^2+\left(\frac{\sqrt{3}}{2}\right)^2}\right\} - \mathcal{L}^{-1}\left\{\frac{ \frac{1}{2}}{\left(s + \frac{1}{2}\right)^2+\left(\frac{\sqrt{3}}{2}\right)^2}\right\}$

 

[PA3040D]

Hi Dear Thanks for grate help

I finalize the answer as per your advise
Please advise

Is my last row correct as well as others


And another small question please advise how insert math function like you have typed , I searched the forum not found the help

 

[mario99]

You have to modify this before solving it.

$\displaystyle \mathcal{L}^{-1}\left\{\frac{ \frac{1}{2}}{\left(s + \frac{1}{2}\right)^2+\left(\frac{\sqrt{3}}{2}\right)^2}\right\}$

 

[mario99]

And another small question please advise how insert math function like you have typed , I searched the forum not found the help

If you want to write mathematical symbols, you should learn Latex code. It is not difficult, but if you make one mistake in the code, it takes time to find it and correct it.