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Dipole Oscillation İn Electric Field

  1. Mar 13, 2017 #1
    1. The problem statement, all variables and given/known data
    Electric Dipole makes small oscillation is electric field find its ##ω##

    2. Relevant equations
    ##τ=pEsinθ##
    ##τ=I∝##

    3. 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)
     
  2. jcsd
  3. Mar 14, 2017 #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.
     
    Last edited: Mar 14, 2017
  4. Mar 14, 2017 #3
    not really
     
  5. Mar 14, 2017 #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.
     
  6. Mar 14, 2017 #5
    I see now..Sure it does.But Hıw can I go from this info to ω
     
  7. Mar 14, 2017 #6

    kuruman

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    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. Mar 14, 2017 #7
    İt s ##w=\sqrt \frac {pE} {I}## ?
     
  9. Mar 14, 2017 #8

    kuruman

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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

    $$\frac{d^2(something)}{d(something ~else)^2}=-(frequency)^2 \times (something)$$
     
  10. Mar 14, 2017 #9
    thanks
     
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