GREPhysics.NET: GR0177 #59

GR0177 #59

Problem

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Electromagnetism $\Rightarrow$ }LC Circuit

The form for a simple harmonic oscillator is $m\ddot{x} + kx =0$ , which one can obtain from Hooke's Law. Comparing this to the LC circuit equation $L\ddot{Q}+Q/C=0$ , one sees that $L \Leftrightarrow m$ and $1/C \Leftrightarrow k$ and $Q \Leftrightarrow x$ . This is choice (B).

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Comments

theperiodictable
2014-10-23 11:05:59

One good thing to consider for this problem is the following: the only thing you can have a derivative of is x, since m and k are constants, so Q must be x.

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bslugger360
2013-08-11 16:21:51

Another thought that helped me was looking at the energy of a spring and the energy of a capacitor:

$U_{capacitor} = \frac{Q^2}{2C}$

$U_{spring} = \frac{kx^2}{2}$

From this it's pretty clear that Q $\Rightarrow$ x and C $\Rightarrow$ 1/k, making B the only possible answer.

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mrTrig
2010-11-09 00:43:49

Something nice to remember $\omega = \frac{1}{\sqrt{LC}}$ for LC Circuits. And from hook's $\omega = \sqrt{\frac{k}{m}}$ . Thus L and C must be inversely related and must be related to either $k$ or $m$ . Only B satisfies.

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carl_the_sagan
2008-11-07 19:48:26

A really cheesy way is to totally disregard the question and just look at the answers. Typically on a question like this they are going to have to repeat the correct value for each column a few times.

so "m" is repeated in L, "1/k" is repeated in C, and "x" is repeated in Q. The only answer which lines all these multiple-occurring rows is B.

Granted this has nothing to do with physics, but this isn't about physics, its about getting the right answer.

amber
2014-10-22 23:27:03

I went with this route too. I figured if there were two that were close I could reason it out, but I didn't have to do that.

UNKNOWNUMBER
2018-10-18 21:06:34

I don\'t think this works all the time--I would say you just got lucky.

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Another thought that helped me was looking at the energy of a spring and the energy of a capacitor: $U_{capacitor} = \frac{Q^2}{2C}$ $U_{spring} = \frac{kx^2}{2}$ From this it's pretty clear that Q $\Rightarrow$ x and C $\Rightarrow$ 1/k, making B the only possible answer.

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