"Finally, discuss some physical limitations that might ..."

Jamin2112

1. The problem statement, all variables and given/known data

Part (d) of problem 1 here: http://faculty.washington.edu/joelzy...02_W13_hw4.pdf
2. Relevant equations

I have (I(t) I'(t))^T = cos(t/√(LC))k₁ + sin(t/√(LC))k₂, some k₁, k₂ ε ℂ² for my solution and so I know that decreasing the value of LC increases the ticking frequency of this clock.

3. The attempt at a solution

But I'm at a loss for what to put for this "discuss some physical limitations" thing. Thoughts?

rude man

For one thing - do you think this clock will run forever? Even if so, does the current level stay constant or does it get harder to detect over time? Do the values of R, C and L change in any way over time?

Jamin2112

Theoretically, yes.

Well, it oscillates, since current is V = RI, R is constant, I is oscillating.

I don't really know since I'm not an electrical engineer

voko

I do not see any dependence of the solution on R. How come?

Jamin2112

If we want it to tick with a constant frequency, then we want the node to be a center, so we want R=0. Right? We want I(t)=0 periodically.

rude man

Does it seem reasonale to assume that whatever circuit you use to detect the zero crossings of the current has a limitation as to how low the current can be before it can't tell the difference between that low level and zero?

And BTW you can't have R = 0 in real life. Besides, the problem specifies a resistor.

And FYI R, C and L do change over time & environment. That's why crystal oscillators are used in your PC!

voko

Do you think it is physically possible to have R = 0? The circuit is called LRC for a reason.

Jamin2112

Isn't my intuition right, though, that we want the vector field of (I I')^T to be something circling the origin forever?

voko

Is that possible with R > 0?