3.2 Calculation

Course subject(s) 3. Extending the model

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

\begin{array}{rclr} C \frac{d V}{d t} & = & I (t), & V (0) = 0, \\ L \frac{d I}{d t} & = & V_{B} - R I (t) - V (t), & I (0) = 0. \end{array}

Constants $V_{B}, L$ and $R$ are given: $V_{B} = 5$ V, $L = 0.004 μ$ H, $R = 0.1 Ω,$ and $C$ has to be found such that the circuit oscillates with at frequency of $100$ MHz $= 10^{8}$ Hz.

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

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