Proof of natural frequency in RCL circuit

[alanchakhin]

I am just wondering what is the proof of the equation
2*pi*f = 1/√(LC)

 

[Simon Bridge]

Welcome to PF;
The relation is derived from the differential equation describing the flow of charge in an ideal RCL circuit.

 

[alanchakhin]

So what is the differential equation describing the flow of charge in an ideal RCL circuit?

 

[sophiecentaur]

I think this link is what you need.

 

[Simon Bridge]

I was going to suggest this one - but that works too. :)

 

[Emilyjoint]

The resonant frequency is when XL = Xc
That is when 2∏fL = 1/2∏fC
When this condition is satisfied V is in phase with I.