# Dipole Oscillation İn Electric Field

Gold Member

## Homework Statement

Electric Dipole makes small oscillation is electric field find its ##ω##

##τ=pEsinθ##
##τ=I∝##

## The Attempt at a Solution

##τ=pEsinθ##
##τ=I∝##
so ##pEsinθ=I∝## which thats in small oscillation becomes,

##pEθ=I∝##
then,
##pEθ=I\frac {dw} {dt}## then

##w=\frac {pE} {I} \int θdt##

I stucked here

(I cant use DE)

kuruman
Homework Helper
Gold Member
What if you rewrote the equation as
$$\frac{d^2 \theta}{dt^2}=-\frac{pE}{I} \theta$$
Does the form look familiar?

On edit: Added negative sign on right side because of restoring torque.

Last edited:
Gold Member
What if you rewrote the equation as
$$\frac{d^2 \theta}{dt^2}=\frac{pE}{I} \theta$$
Does the form look familiar?

not really

kuruman
Homework Helper
Gold Member
Does this look familiar?
$$\frac{d^2 x}{dt^2}=-\frac{k}{m} x$$
Hint: "Not really" is not an option. Think what it could possibly be.

Gold Member
I see now..Sure it does.But Hıw can I go from this info to ω
Does this look familiar?
$$\frac{d^2 x}{dt^2}=-\frac{k}{m} x$$
Hint: "Not really" is not an option. Think what it could possibly be.

kuruman
Homework Helper
Gold Member
I see now..Sure it does.But Hıw can I go from this info to ω
Note that the two diff eqs are the same, except the symbols are different. They have the same solutions.
Compare the right sides of the two equations. What is ω in the familiar equation? What could ω be in the unfamiliar equation?

Gold Member
İt s ##w=\sqrt \frac {pE} {I}## ?

kuruman
Homework Helper
Gold Member
İt s ##w=\sqrt \frac {pE} {I} ##?
Yep. Remember this and learn to recognize the simple harmonic oscillator equation in all its different disguises. Its general form is

$$\frac{d^2(something)}{d(something ~else)^2}=-(frequency)^2 \times (something)$$

Arman777
Gold Member
Yep. Remember this and learn to recognize the simple harmonic oscillator equation in all its different disguises. Its general form is

$$\frac{d^2(something)}{d(something ~else)^2}=-(frequency)^2 \times (something)$$
thanks