Calculating Frequency in RLC Circuits with Gradual Decay

[juanpablod]

Oscillation frequency

I'm not sure what to do for this question. I have found a few things of relevancy but I'm making the problem more complex than it really is?

A leyden jar of capacitance C=10^-9 farads is short circuited with a copper wire of self-inductance L=3 x 10^-7 and resistance R=5x10^-3 ohms.

find the frequency in cycles per second (angular frequency divided by 2 Pi) of the (gradually decaying) oscillatory current.

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Do i need to use these values in the form ax'' + bx' + cx = f(t). If so what is f(t) meant to represent?

find the number of oscillations per e-folding of the gradual decay. (i.e. in the time that the amplitude reduces from a to a/e).

I'm not sure what this question means, how do the e-foldings relate to this?

Any help is appreciated. I'm fairly sure i could do this question if i knew the relationship. Am i missing the obvious?

Thanks. Pablod

 

[hotvette]

This is electrical circuit analysis. Here are the steps:

1. Draw a picture of the circuit
2. Write the differential equation associated with the circuit
3. Solve the differential equation - it will be a decaying sinusoid

Have you done any circuit analysis?

 

[mezarashi]

find the frequency in cycles per second (angular frequency divided by 2 Pi) of the (gradually decaying) oscillatory current.

There is actually a direct formula for this because RLC circuits are common. However, depending on the intention of the exercise, you should or should not be using it. It all can be derived from first principles, that is circuital laws.

Try doing what hotvette has already suggested if you haven't.