Question

Why is the resonance frequency of an LRC circuit the same equation as the natural frequency of an LC circuit?

Answer 1

generally resonance frequency are the same as the natural frequency of a system.
Think of a simple example of a kid on a swing
Now I push the swing. at What frequency should I push? (If I want my efforts to be efficient)
I gave a push now he goes away and back to me, at the moment of zero velocity is the best moment to push!
now he goes further away, but the period stays the same! (for small angles anyway)
thats the peroid of the natural frequency of the swing.
So if the acting force is at the same frequency as the natural frequency of the system u get an higher and higher amplitude! Thats resonance.
and it is always realated to the natural frequency (not always the same but usually yes)
That is why u can berak a glass of wine by singing a note with the same pitch of the glass (the sound it will make if u hit it)

About the math of it - let someone else do it :)

watch out with the volume!
http://www.youtube.com/watch?v=F8dzsf-NFP4&feature=related

Answer 2

nice question by the way!

Answer 3

What level of mathematics are you familiar with? If you are at the level of an algebra / trigonometry based calculus class, then I'm afraid you'll just have to take our word for it. In fact, you may have to take our word for it anyway unless you are familiar with 2nd order differential equations.

This is similar mathematically (actually, identical) to a damped oscillator, like a mass on a spring moving through water. The "natural frequency" of the system if you like is unchanged by the friction. The frequency with which the system will oscillate all by itself is slower than this, but if you were to apply a driving force with a frequency equal to the "natural frequency" you would achieve resonance.

Answer 4

The techy way of putting it is that L & C both have a complex component while R does not.
I'll try and put that into English: Inductors and Capacitors both change their behaviour depending on the frequency of the current passing through them, Resistors are not frequency dependant.

If you put a unit pulse input into the circuit and then walk away (kick the swing and leave it) then you will see the natural response. If you keep applying a force (electromotive for the circuit or motive for the swing) then the resonance will be a combination of your applied force and the natural resonance of the system.