LC Oscillations, Quantitatively — Question 2

Question 2

An energy-transfer clock runs at twice the charge frequency

An LC loop is released with q=Q and i=0. Its measured capacitor energy repeats every .800 ms. The inductance is .0400 H.

1. Find the charge period, angular frequency, and capacitance.

2. Find the first time after release at which the two field energies are equal.

Question 2 - Solution

An energy-transfer clock runs at twice the charge frequency

(a) Method and calculation

$$U_C=U\cos^2\omega t\Rightarrow T=2(.800\,ms)=1.600\,ms.$$$$\boxed{\omega=2\pi/T=3926.99\,s^{-1},\quad C=(\omega^2L)^{-1}=1.62114\,\mu F}.$$

(b) Interpretation and further calculation

$$\cos^2\omega t=1/2\Rightarrow\omega t=\pi/4\quad\text{first occurrence}.$$$$\boxed{t=T/8=.200\,ms}.$$

Physical check

Mistaking the energy repetition time for T gives a capacitance four times too small.