Dipole Oscillation İn Electric Field

[Arman777]

Homework Statement

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

Homework Equations

$τ=pEsinθ$
$τ=I∝$

The Attempt at a Solution

$τ=pEsinθ$
$τ=I∝$
so $pEsinθ=I∝$ which that's in small oscillation becomes,

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

$w=\frac {pE} {I} \int θdt$

I stucked here

(I can't use DE)

 

[kuruman]

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.

 

[Arman777]

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]

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.

 

[Arman777]

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]

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?

 

[Arman777]

İt s $w=\sqrt \frac {pE} {I}$ ?

 

[kuruman]

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]

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