Demonstrate this Hypothesis

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hi
please help me to Demonstrate this Hypothesis

in the RC(RL) circuit all of the natural frequences are real and Negative
 

why would is be negative ?
 

Hi,

If H(p) is a transfer function of a linear passive network (when p=σ+jω), then the poles of H(p) have real part negative (or zero if the network haven't resistors) because the network is passive and then Liapunov stable. If the real part is zero the network is Liapunov unstable but BIBO stable (a LC oscillator is BIBO stable but not liapunov stable).

A pole with positive real part generate unstability, only active network may admits pole with positive real parts.

Best Regards

Ninux
 

mhrm.electronic said:
hi
please help me to Demonstrate this Hypothesis
in the RC(RL) circuit all of the natural frequences are real and Negative
Click to expand...

I think, up to now there is no answer to your question.
Well, here is an answer:

1.) Definition: If a system of second order is exposed to a step function it reacts with a damped sine wave (if the pole Q is larger than 0.5). The frequency of this signal is the "natural frequency".
2.) This frequnecy, of course, is always positive. However, as the amplitude of this signal decreases with time (for a stable system), the damping factor "sigma" is negative. That´s all.
 

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