Is this a P.E.?

**wirefree** · August 7th 2012, 11:03 PM

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}

**Prove It** · August 7th 2012, 11:30 PM

Originally Posted by wirefree

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?

**wirefree** · August 8th 2012, 04:19 AM

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

Apologise, I should have made that clear.

Best Regards,
Wirefree

**Prove It** · August 8th 2012, 04:21 AM

Originally Posted by wirefree

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?

$\displaystyle \begin{align*} \frac{d^2\theta}{dt^2} = -m\,B\,I^{-1}\,\theta \end{align*}$

**wirefree** · August 8th 2012, 05:32 AM

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

**HallsofIvy** · August 8th 2012, 06:39 AM

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.

**wirefree** · August 8th 2012, 10:28 AM

Appreciate it, HallsofIvy.

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

Best Regards,
wirefree

**Prove It** · August 8th 2012, 07:26 PM

Originally Posted by wirefree

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...

**wirefree** · August 10th 2012, 11:41 AM

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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