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Solving Simple Harmonic Motion Problem with Energy

  1. Apr 7, 2010 #1
    1. The problem statement, all variables and given/known data
    A 500g block on a spring is pulled 20cm and released. The motion has a period 0.8s.

    What is the velocity when the block is 15.4cm from the equilibrium?


    2. Relevant equations
    Etotal = 0.5kx2 + 0.5mv2
    w = [tex]\sqrt{k/m}[/tex]
    w = 2pi*f
    f = 1/T

    3. The attempt at a solution

    [FINDING K]
    f = 1/0.8 = 1.25
    w = 2pi*(1.25) = 7.85
    7.85 = [tex]\sqrt{k/0.5}[/tex]
    k = 30.8

    [FINDING TOTAL ENERGY BY USING THE INITIAL VALUES]
    Etotal = 0.5(30.8)(0.2)2
    = 0.616

    [USING THE TOTAL ENERGY WITH THE SECOND SET OF VALUES TO FIND V]
    0.616 = 0.5(30.8)(0.154)2 + 0.5(0.5)(v)2
    x = 1.7

    Make sense to me...just hope its right. Any comments? Thanks as always - I appreciate the effort.
     
  2. jcsd
  3. Apr 7, 2010 #2

    ehild

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    It is all right, up to the last line. What is x? and what is 1.7? And how much is v?

    ehild
     
  4. Apr 7, 2010 #3
    yeah its all good except you missed some calculations. My answer is around 1 I think.
     
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