Damped Oscillations in an RLC circuit

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Homework Help Overview

The discussion revolves around a damped oscillation problem in an RLC circuit, specifically involving a resistor, inductor, and capacitor. The original poster seeks to determine the charge on the capacitor after a specified number of cycles, given initial conditions and relevant equations.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to relate angular frequency to the time required for multiple cycles, expressing confusion about the definition of angular frequency. Some participants clarify that angular frequency is measured in radians per second and relate it to the period of oscillation.

Discussion Status

The discussion is active, with participants providing clarifications regarding angular frequency and its relationship to time. There is an exchange of ideas about calculating the time for multiple cycles, with some guidance offered on using the period in the context of the problem.

Contextual Notes

The original poster indicates a lack of familiarity with mechanics, which may affect their understanding of angular frequency and its application in this context.

electrohau5
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Homework Statement



A single loop circuit consists of a 7.2 ohm resistor, a 11.9 H inductor, and a 3.4*10^-6 F capacitor. Initially the Capacitor has a charge of 6.3*10^-6 C and the current is zero. Find the charge on the capacitor N complete cycles later for N=5.

Homework Equations



2. Homework Equations
q=Qe^(-Rt/2L)cos(wt + p), where p is the phase constant and w is the angular frequency.

The Attempt at a Solution



I have already found angular frequency to be 157.2122, but how do I relate this to time it takes to make 5 cycles? I do not fully understand the definition of w.
(the idea of angular frequency has always been quite confusing to me as I have not yet taken mechanics and am doing E&M first)
 
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electrohau5 said:

Homework Statement



A single loop circuit consists of a 7.2 ohm resistor, a 11.9 H inductor, and a 3.4*10^-6 F capacitor. Initially the Capacitor has a charge of 6.3*10^-6 C and the current is zero. Find the charge on the capacitor N complete cycles later for N=5.


Homework Equations



2. Homework Equations
q=Qe^(-Rt/2L)cos(wt + p), where p is the phase constant and w is the angular frequency.

The Attempt at a Solution



I have already found angular frequency to be 157.2122, but how do I relate this to time it takes to make 5 cycles? I do not fully understand the definition of w.
(the idea of angular frequency has always been quite confusing to me as I have not yet taken mechanics and am doing E&M first)

Angular frequency is radians per second. So 1 rotation per second is 2pi radians per second. Etc.

If you know w which = 2pi * f, then period T = 1/f as you know I'm sure.
 
electrohau5 said:
would the time it takes be equal to 5 times the period, so 10pi/w?

Yes.

ehild
 
electrohau5 said:
would the time it takes be equal to 5 times the period, so 10pi/w?

Yes again.
 

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