This section gives an example of how the model developed earlier could be extended to account for additional knowledge of the system's structure. Again, if you have not yet been exposed to this particular type of mathematical analysis, simply note that all models can be refined as we gain more knowledge about the system. Think back to the model you identified in the last section. How could you extend this model to make it a better reflection of reality?
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.