Help with laplace transformation?
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Having a little trouble with this equation.. can anybody help figure it out?
Much appreciated :)
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Interesting prb. Asked my shifu and he solved it here : www.whitegroupmaths.com/2012/11/problem-21-finding-output-voltage-of-rc.html . :-)
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How about this? It's a different varation posted, looks more demanding though.
Thanks for your help on the first one :) It's nicely done. -
Don't know if he is free to solve this one 4 you, maybe some other physics zai kia in this forum can help u ? Anyways wat level is this?
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Tetiary.
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V_R = V_in + V_C (since voltage at a junction should be single-valued)
=> -iR = sin(wt) + (1/C) (int from -infty to t) i(t') dt'
differentiate the above w.r.t. t :
-(di/dt) R = w cos(wt) + (1/C) i
take Laplace transform here, multiplying both sides by exp(-st) then integrating from 0 to infty:
-Rs L(s) = -s/(s^2+w^2) + (1/C) L(s) where L(s) is the Laplace transform of i(t)
rearrange to obtain
L(s)=( s/R ) ( s^3 + s^2/RC + sw^2 + w^2/RC )
do the usual partial fraction procedure:
L(s)= (1/R) [ (alpha s + beta) / ( s^2 + w^2 ) - alpha / ( s + 1/RC ) ]
where alpha and beta are coefficients I'm too lazy to specify here
Now do the inverse Laplace transform by referring to tables (or if you are masochistic enough, you can do the contour integrals) and you will obtain i(t).
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Ahh, this is awesome, but I havent learnt it yet, for me it will be covered next semmy.
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There's nothing stopping you from learning it now. Wikipedia is your friend.
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simple question, don't ask me lah, go ask your teacher.
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