- #1

bsr25

- 7

- 0

## Homework Statement

The figure opposite shows a free oscillator composed of an LC circuit. Derive an expression for the resonance frequency. Show all of your working.

## Homework Equations

d

^{2}x/dt

^{2}+ ω

^{2}x = 0

## The Attempt at a Solution

First I tried using Kirchoffs Voltage Law to set up a differential equation defining the circuit.

L(d

^{2}q/dt

^{2}) + Q

_{1}/C + Q

_{2}/C = 0

I then combined the two voltages across the capcitor, and divided by L

(d

^{2}q/dt

^{2}) + Q

_{Total}/LC = 0

Comparing this to the equation for SHM:

d

^{2}x/dt

^{2}+ ω

^{2}x = 0

shows that ω

^{2}= 1/LC.

But I figure this cannot be the case as that is the result expected for a simple LC circuit with one inductor and one capcitor. As this is two capcitors and one inductor I figure the rsult must be different.

One thing I notice on the diagram is the Capcitors have both negative plates facing each other, I wasnt sure what effect if any this would have on the circuit.

Other than this attempt at a solution which I am fairly sure if way off, I am a bit lost. Any help towards reahcing the right answer would be greatly appreciated!

Thanks