Harmonic oscillations and electric dipoles

[PinkFlamingo]

Hi there, I was hoping that someone would be kind enough to help me out with this question. I don't even know where to start

Use T=Ia (where T=torque) to show that if an electric dipole with dipole moment of magnitude p and moment of inertia I is oriented with its dipole moment making a small angle theta with the direction of an external electric field of magnitude E, the dipole will execute simple harmonic oscillations about the field direction with a frequency v given by:

v= [1/(2pi)] [(pE)/I]^1/2

 

[turin]

The dipole moment and electric field will give you the torque, which is the L.H.S. of the equation τ = I α. (Big hint: it will involve orientation as a function of time, θ(t))

For the R.H.S., you need to replace angular acceleration α with a second order derivative. (Big hint: it will involve orientation as a function of time, θ(t))

Then, solve the diff. eq. The solution should be sinusoidal (with a frequency, ν).

 

[PinkFlamingo]

I'm sorry... I'm still lost. I have no idea how to do any of that. How do you take the derivative if you don't know the value?

 

[PinkFlamingo]

ok I figured it out! Thanks for your help!

 

[turin]

ok I figured it out!

Very cool. However, I am curious:


How did you go from:

I have no idea how to do any of that.

to:

ok I figured it out!

?