hello everybody
there is some problem in Laplace :

if do Laplace by alpha is different by my hand why?

by alpha


by my hand

 

Check your simplification.

You should have

\( \frac {40}{s^2+6s+12}=\frac {40}{ \(s+3\)^2+\({\sqr {3}}\)^2\)

 

Check your simplification.

You should have

\( \frac {40}{s^2+6s+12}=\frac {40}{ \(s+3\)^2+\({\sqr {3}}\)^2\)

yes , if use calculator will get (-3+1.732j) , (-3-1.732j)
thanks

 

yes , if use calculator will get (-3+1.732j) , (-3-1.732j)
thanks

A calculator isn't necessary. The manipulation in post #2 should be readily appreciated by the observant student.

 

yes , if use calculator will get (-3+1.732j) , (-3-1.732j)
thanks

You need to become familiar with completing the square. You also need to stop relying on tools like Wolfram Alpha and a calculator to do your thinking for you. It's one thing to use them to verify your work or to ease the grunt work, it's another to just turn to them because you can't work it out yourself. The distinction between proper and improper use of these kinds of tools is very gray and malleable, but you want to try to develop and maintain your ability to do your own thinking.

 

... you want to try to develop and maintain your ability to do your own thinking.

The mind needs to solve complex logic problems to remain sharp... pretty much like muscles need a basic level of weight lifting to keep functional and the rest of the body in good shape...