## shafqat_uet 2 years ago Can anyone find inverse Laplace of this (s^2-pi^2)/(s^2+pi^2)^2

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1. shafqat_uet

$\frac{(s^{2}-\pi ^{2})}{(s ^{2}+\pi ^{2})^{2}}$

2. itsmylife

$\frac{ (s- \pi) (s+ \pi)}{ (s+ \pi) (s+ \pi) }$ now you can do it ;)

3. Callisto

The denominator is not quite right?

4. shafqat_uet

thanks itsmylife

5. itsmylife

i think its done , you gotta separate terms now thats all ;) your welcome @shafqat_uet

6. itsmylife

holda thers a mistake

7. shafqat_uet

in denomirator you made a mistake

8. itsmylife

$\frac{ (s - \pi)(s + \pi) }{ (s^2 + \pi^2)(s^2+ \pi^2) }$ this looks pretty easier but m stuck now :(

9. Callisto

$\frac{(s^{2}-\pi ^{2})}{(s ^{2}+\pi ^{2})^{2}}$$=\frac{(s^{2})}{(s ^{2}+\pi ^{2})^{2}} - \frac{\pi^2}{{(s ^{2}+\pi ^{2})^{2}}}$ $=(\frac{s^2}{(s ^{2}+\pi ^{2})})(\frac{1}{(s ^{2}+\pi ^{2})}) - \frac{\pi^2}{{(s ^{2}+\pi ^{2})}}\times \frac{1}{{(s ^{2}+\pi ^{2})}}$

10. shafqat_uet

@itsmylife good try but I have also tried like this. Is it possible using derivative or integral of the laplace

11. itsmylife

no i guess wat @Callisto has done is quite easier , you gotta take inverse now

12. Callisto

Sorry, last step: $=(\frac{s}{(s ^{2}+\pi ^{2})})(\frac{s}{(s ^{2}+\pi ^{2})}) - \frac{\pi}{{(s ^{2}+\pi ^{2})}}\times \frac{\pi}{{(s ^{2}+\pi ^{2})}}$