Halliday, Resnick & Walker — Electromagnetic Oscillations and Alternating Current: Problem 34

34 An inductor is connected across a capacitor whose capacitance can be varied by turning a knob. We wish to make the frequency of oscillation of this LC circuit vary linearly with the angle of rotation of the knob, going from $2 \times 10^5$ to $4 \times 10^5 \text{ Hz}$ as the knob turns through $180^\circ$. If $L = 2.0 \text{ mH}$, plot the required capacitance $C$ as a function of the angle of rotation of the knob.