Within what limits should the inductance of the coil of the oscillating circuit change

Within what limits should the inductance of the coil of the oscillating circuit change so that oscillations from 400 to 500 Hz can occur in it at c = 10 μF

To find the limits of the oscillation of the inductance of the indicated coil of the oscillatory circuit, we use the formula: νx = 1 / (2Π * √ (Lx * C), whence we express: Lx = 1 / (νx ^ 2 * 4 * Π ^ 2 * C).

Variables: ν1 – the first vibration frequency (ν1 = 400 Hz); ν2 – second vibration frequency (ν2 = 500 Hz); C – electrical capacity of the circuit (C = 10 μF = 10-5 F).

Calculation: a) L1 = 1 / (ν1 ^ 2 * 4 * Π ^ 2 * C) = 1 / (400 ^ 2 * 4 * 3.14 ^ 2 * 10-5) = 0.016 H = 16 mH;

b) L2 = 1 / (ν2 ^ 2 * 4 * Π ^ 2 * C) = 1 / (500 ^ 2 * 4 * 3.14 ^ 2 * 10-5) = 0.01 H = 10 mH.

Answer: The inductance of the indicated coil should vary from 10 mH to 16 mH.