Low Pass Filter Transfer Function
You are effectively solving a second order filter as the first capacitor is in parallel with Vin. There is nothing that C1 can do, it can have a lower impedance at higher frequencies but then voltage source Vin would simply deliver more current. You could remove C1 and at Vout nothing would change.







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This is how such a filter is really supposed to be used.
Note that I added R1 which allows C1 to do some low-pass filtering.







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