# Laplace transform

Discussion in 'Math' started by ashmeo, Jun 24, 2012.

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1. ### ashmeo Thread Starter New Member

Nov 21, 2011
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Hi everyone, I've been given a problem and I can't seem to prove it. The picture shows a filter, ( i think its a low pass filter) [pic attached]

Here's what i got so far.

I've got Vr=iR
Vc= Vin(1-e^-t/RC)

Vin=Vr+Vc
= iR + Vin(1-e^-t/RC)
= iR + sinwt(1-e^-t/RC)

since Vr=Vout, and Vin = sinwt

sinwt = Vout + sinwt(1-e^-t/RC)

Vout= sinwt - sinwt(1-e^-t/RC)

am i suppose to laplace this?

If yes,

and when i laplace Vin=Vr+Vc as stated in the hint , i got L{vin} = iR/s + w/(s^2 + w^2) + w/ [ (s+1/RC)^2 +w^2 ]

how am i supposed to continue and relate to proving Vout?

tell me what to do step by step as im still a beginner and thanks for your replies! I appreciate it

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2. ### t_n_k AAC Fanatic!

Mar 6, 2009
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It's poor practice to start several threads on exactly the same topic. It leads to confusion and frustration.

3. ### Wendy Moderator

Mar 24, 2008
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ashmeo likes this.