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

 

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

 

One thread is enough.

laplace transform in RC circuit