Frequency of an electric dipole

[LittleLu609]

Homework Statement

Find the frequency of oscillation of an electric dipole, of dipole moment p and rotational inertia I, for small amplitudes of oscillation about its equilibrium position in a uniform electric field of magnitude E.

Answer: [(pE/I)^0.5]/(2*pi)

Homework Equations

I think that the relevant equations are τ = I α , τ = pEsinθ , and α is the second derivative of θ

The Attempt at a Solution

τ = I α
pEsinθ = I d2θ/dt2
Then I don't know where to go on from there. Am I even on the right track? Help?

 

[SammyS]

Homework Statement

Find the frequency of oscillation of an electric dipole, of dipole moment p and rotational inertia I, for small amplitudes of oscillation about its equilibrium position in a uniform electric field of magnitude E.

Answer: [(pE/I)^0.5]/(2*pi)

Homework Equations

I think that the relevant equations are τ = I α , τ = pEsinθ , and α is the second derivative of θ

The Attempt at a Solution

τ = I α
pEsinθ = I d2θ/dt2
Then I don't know where to go on from there. Am I even on the right track? Help?

For small values of θ, sin(θ) ≈ θ.

 

[LittleLu609]

For small values of θ, sin(θ) ≈ θ.

Oh, thanks! That's a big help! So from there, do I integrate the equation to solve for dθ/dt since dθ/dt = w? Then to find f I divide w by 2*pi?

EDIT: Nevermind, yay, I finally solved the problem! Thanks again for the help.