Angular Frequency and Resonance Frequency

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Angular frequency is defined as (2)(pi)(frequency) and can be calculated using the formula 1/square root(LC) at resonance frequency. The resonance frequency is an inherent property of the circuit, independent of whether a signal is present. In passive circuits, the input frequency remains unchanged, while the circuit can only affect the amplitude of the signal. When multiple frequencies are present, the passive circuit can selectively attenuate frequencies, favoring those near its resonance frequency. Therefore, the equation for angular frequency is applicable primarily at resonance.
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For the equation, angular frequency =(2)(pi)(resonance frequency)= 1/square root (LC), can this also be used when a circuit is not at resonance frequency?


Thanks
 
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Of course angular frequency =(2)(pi)(frequency), always.
The second part, 1/square root (LC) depends what you mean.
The resonance frequency is a property of the circuit, irrespective of whether there is any signal going through the circuit. A passive circuit cannot change the frequency of the input signal, but it can change its amplitude. The frequency in the passive circuit will always be the input frequency, the resonance frequency is irrelevant.

(Of course if the input has many frequencies, the passive circuit can attenuate some of them while mostly passing just the ones close to its resonant frequency. )
 

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