Practice problem (Clock!)

Calculation

The system of differential equation for the LC-oscillator is:

\(c\dfrac{dV}{dt} = I(t)\), \(V(0) = 0\),

\(L \dfrac{dI}{dt} = V_B - RI (t) - (t) \), \(I(0) =0\).

Constants VB,L and R are given: VB=5V, L=0.004μH, R=0.1Ω, and C has to be found such that the circuit oscillates with at frequency of 100MHz =108Hz.

First, we need to choose a time scale, and then we have to scale the problem and choose an appropriate step size.