The charge on the capacitor plates of an ideal oscillatory circuit changes over time according to the law

The charge on the capacitor plates of an ideal oscillatory circuit changes over time according to the law q = 100cos10 ^ 3 pi t (mlC) determine the period of electromagnetic oscillations

The charge q on the capacitor plates of an ideal oscillatory circuit changes over time t according to the law q = Q ∙ cos (ω ∙ t), where Q is the amplitude value of the charge on the capacitor plates, ω is the cyclic frequency of charge oscillations. It is determined by the formula: ω = 2 ∙ π / T, we get:

q = Q ∙ cos (2 ∙ π / Т) ∙ t.

From the condition of the problem it is known that the charge on the capacitor plates changes according to the law:

q = 100 ∙ cos (10 ^ 3 ∙ π ∙ t) mC.

To determine the period of electromagnetic oscillations, compare the formulas and equate the coefficients at t, we obtain

2 ∙ π / Т = 10 ^ 3 ∙ π;

T = 0.002 s = 2 ms.

Answer: the period of electromagnetic oscillations is 2 ms.