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Finally, discuss some physical limitations that might ...

by Jamin2112
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Jamin2112
#1
Feb6-13, 01:44 PM
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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?
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rude man
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Feb6-13, 01:54 PM
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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
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Feb6-13, 02:08 PM
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Quote Quote by rude man View Post
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
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Feb6-13, 02:54 PM
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Finally, discuss some physical limitations that might ...

I do not see any dependence of the solution on R. How come?
Jamin2112
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Feb6-13, 03:28 PM
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Quote Quote by voko View Post
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
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Feb6-13, 03:43 PM
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Quote Quote by Jamin2112 View Post
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
#7
Feb6-13, 04:08 PM
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Quote Quote by Jamin2112 View Post
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
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Feb6-13, 04:45 PM
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Quote Quote by voko View Post
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
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Feb6-13, 05:09 PM
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Is that possible with R > 0?


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