# Thread: Is this a P.E.?

1. ## 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.

Best regards,
wirefree

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

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.

Best regards,
wirefree
Are m, B and I constants?

3. ## 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

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

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.

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*}

5. ## 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 $\frac{d\theta}{dt}$

Best regards,
wirefree

6. ## 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.

7. ## 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

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

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...

9. ## 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