Hey guys.
I was wondering if someone could show me the working out (simplification) for these two equation. This isn't a homework question... just study. If more information is needed... let me know

1)

2)

thanks guys

 

Hey guys.
I was wondering if someone could show me the working out (simplification) for these two equation. This isn't a homework question... just study. If more information is needed... let me know

1)

2)

thanks guys

For 1,

\(\frac{5}{s+2} = \left( \frac{s+1}{2s+1} \right)V_{o}\)

\(\frac{ 5 \times (2s+1)}{(s+2)(s+1)} = V_{o}\)

\(\Rightarrow \frac{10s+5}{(s+2)(s+1)} = V_{o}\)

Or if you're confused by the first simplification,

\(\frac{V_{o}}{2s+1} + \frac{V_{o}}{2 + \frac{1}{s}}\)

\(= \left( \frac{1}{2s+1} + \frac{1}{\frac{2s+1}{s}} \right)V_{o}\)

\(= \left( \frac{1}{2s+1} + \frac{s}{2s+1} \right)V_{o}\)

\(= \left( \frac{s+1}{2s+1} \right)V_{o}\)

If I have time later I will look through the 2nd one as well. (It's the same type of algebra, nothing difficult)

 

ah thats great!
Yeah I understand its simple... I just haven't worked with such fractions in a long time.
If you do have time to do the second one later that would be great.
Thanks for the help

 

You need to take it in steps. First step is to eliminate the 2/S denominator by multiplying both the top and bottom of the second term with S/2

Such that we have:

\(\frac{3}{S} -Vo\ \ -\frac{1}{2}-\frac{SVo}{2}\ \ +\frac{4}{S}-Vo\ \ =\ \ 0\)

Collecting the terms with Vo on one side we get

\( 2Vo+\frac{S}{2}Vo\ \ =\ \ \frac{7}{S} - \frac{1}{2}\)

Multiplying both sides by 2 and simplifying:

\(\Rightarrow\ \ \ \ Vo(4+S)\ \ =\ \ \frac{14-S}{S}\)

\(\Rightarrow\ \ \ \ Vo\ \ =\ \ \frac{14-S}{S(S+4)}\)

 

aaah! I got it!

 

I thought you had to solve for something in here, but this is a plug-in-the-values type of equation.
Not much simplification, really.
It's more like a formula. It is a formula...

 

I thought you had to solve for something in here, but this is a plug-in-the-values type of equation.
Not much simplification, really.
It's more like a formula. It is a formula...

Its a Laplace transformation question. I need to arrange the equation in terms of Vo and use partial fraction to determine the Laplace transformation.

 

You "just" need to find the common abominator.
Eric