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- Aug 7th 2012, 11:03 PM #1

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## Is this a P.E.?

I am very rusty and so out of university.

d^{2}Theta - mB I^{-1}Theta

______ =

dt^{2 }^{ The above is a restoring torque equation of a dipole in a magnetic field. What is the above and how do I solve it? I'd be glad to solve for d Theta / d t. Would appreciate advise. Best regards, wirefree}

- Aug 7th 2012, 11:30 PM #2

- Aug 8th 2012, 04:19 AM #3

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- Aug 8th 2012, 04:21 AM #4

- Aug 8th 2012, 05:32 AM #5

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- Aug 8th 2012, 06:39 AM #6

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## Re: Is this a P.E.?

A "D. E.", or "differential equation", is any equation which involves derivatives of an unknown function. Yes, this is a differential equation. It is, in fact, a "second order linear differential equation with constant coefficients" which are comparatively simple. Here, the differential equation is . It's "characteristic equation" is which has roots . The general solution to the differential equation is where and are constants that can be determined by additional conditions.

- Aug 8th 2012, 10:28 AM #7

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- Aug 8th 2012, 07:26 PM #8

- Aug 10th 2012, 11:41 AM #9

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## Re: Is this a P.E.?

Appreciate all the assistance. This forum never fails! You guys are leaders.

Just to wrap this one up: The general solution will be a function of theta & t. To know the constants C1 & C2, I need some initial/boundary value condition. If I have those, theta can be arrived at. Once arrived at, differentiating it w.r.t. t, will furnish my original requirement 'd theta/d t'.

Don't bother yourself with replying if my above understanding is more or less correct.

You guys rock.

Best regards,

wirefree