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Math Help - Is this a P.E.?

  1. #1
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    Is this a P.E.?

    I am very rusty and so out of university.

    d2Theta - mB I-1 Theta
    ______ =
    dt2


    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
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  2. #2
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    Re: Is this a P.E.?

    Quote Originally Posted by wirefree View Post
    I am very rusty and so out of university.

    d2Theta - mB I-1 Theta
    ______ =
    dt2


    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
    Are m, B and I constants?
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  3. #3
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    Re: Is this a P.E.?

    Yes, Prove It. All three - m, B, and I - are constants.

    Apologise, I should have made that clear.

    Best Regards,
    Wirefree
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  4. #4
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    Re: Is this a P.E.?

    Quote Originally Posted by wirefree View Post
    I am very rusty and so out of university.

    d2Theta - mB I-1 Theta
    ______ =
    dt2


    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
    Just so we're clear, is this the DE?

    \displaystyle \begin{align*} \frac{d^2\theta}{dt^2} = -m\,B\,I^{-1}\,\theta \end{align*}
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  5. #5
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    Re: Is this a P.E.?

    Yes, it is a D.E.; I was hoping you would comment on that. My physics text just states it as is.

    What I would like to arrive at is the value of \frac{d\theta}{dt}


    Look forward to your response.


    Best regards,
    wirefree
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  6. #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 \frac{d^2\theta}{dt^2}= -mBI^{-1}\theta. It's "characteristic equation" is r^2= -mBI^{-1} which has roots r= \pm i\sqrt{mBI^{-1}}. The general solution to the differential equation is C_1cos(\sqrt{mBI^{-1}}t)+ C_2sin(\sqrt{mBI^{-1}}t) where C_1 and C_2 are constants that can be determined by additional conditions.
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  7. #7
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    Re: Is this a P.E.?

    Appreciate it, HallsofIvy.

    To my concern, is there a procedure to arrive at \frac{d\theta}{dt}?


    Best Regards,
    wirefree
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  8. #8
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    Re: Is this a P.E.?

    Quote Originally Posted by wirefree View Post
    Appreciate it, HallsofIvy.

    To my concern, is there a procedure to arrive at \frac{d\theta}{dt}?


    Best Regards,
    wirefree
    Surely if you can solve the DE to get \displaystyle \begin{align*} \theta \end{align*}, you can get \displaystyle \begin{align*} \frac{d\theta}{dt} \end{align*} by differentiating...
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  9. #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
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