Dipole Oscillation İn Electric Field

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  • #1
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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 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)
 

Answers and Replies

  • #2
kuruman
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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.
 
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  • #3
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What if you rewrote the equation as
$$\frac{d^2 \theta}{dt^2}=\frac{pE}{I} \theta$$
Does the form look familiar?

not really
 
  • #4
kuruman
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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.
 
  • #5
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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.
 
  • #6
kuruman
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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?
 
  • #8
kuruman
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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

$$\frac{d^2(something)}{d(something ~else)^2}=-(frequency)^2 \times (something)$$
 
  • #9
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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
 

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