# exponential term in RLC sinusoidal analysis

I was learning to work with RLC circuits with sinusoidal excitations and the book I was dealing with showed me that the responses of these passive elements to sinusoidal excitation were themselves purely sinusoidal and hence phasor digarams were the best way to deal with these elements, but then I tried solving a simple series RLC circuit using laplace/complex frequency analysis and I landed myself a sine term, a cosine term and a real exponential term. I don't know what or why I am getting that real exponential term, I tried to do it over and over and I got the same results. I am pretty sure my calculations are correct but the book mentions nothing about the exponential term. Kindly pitch in...

This is the circuit I was talking about

simulate this circuit – Schematic created using CircuitLab

Here is an image for a KVL and laplace transformation

Here is an image for the inverse after separation. I dont think there is a mistake

• Why don't you show us the circuit you are trying to analyze and the work that you have done? My internet connection is too slow to read your mind. Mar 22, 2014 at 13:04
• I uploaded the circuit, will upload my equations in a minute... Mar 22, 2014 at 13:23
• Where is the "L" in your circuit? The circuit you provided doesn't have an inductor, but you said it was a series RLC circuit. Mar 22, 2014 at 13:43
• No, for this circuit there is no L, just a R and a C and sinusoidal excitation. Mar 22, 2014 at 13:45
• Clearly you have tried to solve this on your own, and your work is incredibly neat for a student. You certainly do not look foolish. But as Dave Tweed said, this isn't a good place for the kind of tutorial you need. I would suggest that you look for circuit analysis books at your school's library. Even pretty old books would cover this material. Mar 22, 2014 at 14:01