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Energy of the Simple Harmonic Oscillator

  1. Jan 3, 2009 #1
    A 50.0-g mass connected to a spring with a force constant
    of 35.0 N/m oscillates on a horizontal, frictionless
    surface with an amplitude of 4.00 cm. Find the speed of the mass
    when the displacement is 1.00 cm.

    Can I use here something like :

    [tex]\frac{mv2}{2}[/tex]=0,5kx2


    ????
     
  2. jcsd
  3. Jan 3, 2009 #2

    Doc Al

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    Staff: Mentor

    Use conservation of energy. What's the total energy at any point in the motion?
     
  4. Jan 3, 2009 #3
    The total energy is 0,5kA2=0,028

    But how to express an energy at displacement 1cm? :blushing:
     
  5. Jan 3, 2009 #4

    Doc Al

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    Hint: Total mechanical energy is the sum of kinetic and potential energy.
     
  6. Jan 3, 2009 #5
    Yes i know that but there is no formula with velocity...

    I've got to use mv2/2??
     
  7. Jan 3, 2009 #6

    Doc Al

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    Staff: Mentor

    Yes, that's the kinetic energy. What's the potential energy at any point?
     
  8. Jan 3, 2009 #7
    Potential energy is 0?
     
  9. Jan 3, 2009 #8

    Doc Al

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    No. Hint: Potential energy is zero when x = 0 and maximum at x = A. What's the PE at an arbitrary position?
     
  10. Jan 3, 2009 #9
    Your equation defines a condition when a half of the energy is in speed and another half in the displacement.
    Ek + Ep = E
    E = kA2/2
    mv2/2 = E - kx2/2
     
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