- #1
Nikarasu M
- 17
- 0
Hello all,
I'm working through old exams for an electrical subject (no solutions given) and I think I've gone wrong somewhere and been left with something I'd like to learn how to work with anyway:
From the last step I can do partial fractions and inverse Laplace etc...
But I got that factorisation via matlab, I can see it obviously works, and given a guess at a factor of the denominator of the 2nd to last line I can see that '+1' would be involved so a next guess might be '(s+1)' and then I'd see if I get zero remainder with polynomial long division, and I'd win in this case, but it was just a lucky guess.
Ok, time for the question: what is the direct method for doing this ?
I left the earlier working up the case we could hijack the math earlier in the process.
I'm working through old exams for an electrical subject (no solutions given) and I think I've gone wrong somewhere and been left with something I'd like to learn how to work with anyway:
[itex]\frac{50}{(s+\frac{1}{s}+1)^2-s^2}[/itex]
[itex]\frac{50}{2s+3+\frac{2}{s}+\frac{1}{s^2}}\times \frac{s^2}{s^2}[/itex]
[itex]\frac{50s^2}{2s^3+3s^2+2s+1}[/itex]
[itex]\frac{50s^2}{(s+1)(2s^2+s+1)}[/itex]
[itex]\frac{50}{2s+3+\frac{2}{s}+\frac{1}{s^2}}\times \frac{s^2}{s^2}[/itex]
[itex]\frac{50s^2}{2s^3+3s^2+2s+1}[/itex]
[itex]\frac{50s^2}{(s+1)(2s^2+s+1)}[/itex]
From the last step I can do partial fractions and inverse Laplace etc...
But I got that factorisation via matlab, I can see it obviously works, and given a guess at a factor of the denominator of the 2nd to last line I can see that '+1' would be involved so a next guess might be '(s+1)' and then I'd see if I get zero remainder with polynomial long division, and I'd win in this case, but it was just a lucky guess.
Ok, time for the question: what is the direct method for doing this ?
I left the earlier working up the case we could hijack the math earlier in the process.