- #1
Antoha1
- 16
- 2
- Homework Statement
- The oscillatory circuit consists of a coil with inductance L = 40 mH and a capacitor with capacitance C=0.25 µF. The active resistance of the circuit is R = 4.0 Ω. Determine how many times the amplitude of the oscillations decreases when a time equal to one oscillation period elapses.
- Relevant Equations
- ##α=\frac{R}{2L},ω_{0}=\frac{1}{\sqrt{LC}}
,ω_{d}=\sqrt{ω_{0}^2−α^2}
,A(t)=A_{0}e^{−αt.}##
Hello. I do not have any literature on this topic because I am still in school and I have not solved any problems about damping vibrations. In school we do not dig into damping vibrations.
But I have dug deeper into it on the internet and found some relevant equations but I am still not sure about how exactly does it work.
So basically, I am thinking that I need damping time period ##T=\frac{2\pi}{\omega_{d}}## and put it this equation ##A(t)=A_{0}e^{−αt.} \Rightarrow \frac{A(T)}{A_{0}}=e^{−αT}##
Also, what I am concerned about is damping because I have found that in series it is α=R/2L and in parallel α=1/2RC, so this is the point where I think searching other ways of solution would be necessary.
But I have dug deeper into it on the internet and found some relevant equations but I am still not sure about how exactly does it work.
So basically, I am thinking that I need damping time period ##T=\frac{2\pi}{\omega_{d}}## and put it this equation ##A(t)=A_{0}e^{−αt.} \Rightarrow \frac{A(T)}{A_{0}}=e^{−αT}##
Also, what I am concerned about is damping because I have found that in series it is α=R/2L and in parallel α=1/2RC, so this is the point where I think searching other ways of solution would be necessary.