Finally, discuss some physical limitations that might

[Jamin2112]

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

Homework Statement

Part (d) of problem 1 here: http://faculty.washington.edu/joelzy/402_502_W13_hw4.pdf

Homework 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.

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]

For one thing - do you think this clock will run forever?

Theoretically, yes.

Even if so, does the current level stay constant or does it get harder to detect over time?

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

Do the values of R, C and L change in any way over time?

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]

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

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]

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

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]

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.

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

 

[Jamin2112]

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

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?