The oscillating circuit and electromagnetic oscillations

Oscillation of a quantity according to a sine or cosine law is called harmonic oscillation; the greatest modulus of the quantity is the amplitude. If at the start the capacitor holds the charge qₘ, the charge changes as q = qₘcos2πνt, the voltage as u = q/C = Uₘcos2πνt and the current as i = Iₘsin2πνt = Iₘcos(2πνt + π/2). Charge and voltage oscillate in phase, while the current leads them by π/2 (a quarter of a period): when charge and voltage are greatest the current is zero, and vice versa. In a real circuit R ≠ 0, the heat Q = I²Rt is released, so the total energy decreases and the amplitude dies away (damped oscillations); the larger R, the faster the damping, and the period increases slightly. Damped oscillations are not strictly harmonic, though for small R they are close to harmonic.