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Homework Help: Oscillations - Finding Displacement at a Speed, Given Displacement at Another Speed

  1. Apr 6, 2010 #1
    1. The problem statement, all variables and given/known data
    A 0.10kg mass is on a spring with k = 0.10 N/m. At time t=0s it crosses x=0m with a velocity of 2.0m/s. What is its displacement when v=1.0m/s?

    2. Relevant equations
    x(t) = Acos(wt + [tex]\varphi[/tex])
    v(t) = -wAsin(wt + [tex]\varphi[/tex])
    w = [tex]\sqrt{k/m}[/tex]

    3. The attempt at a solution
    According to the question...shouldn't v(0) = 2? When a plug those numbers into the v(t) equation I get: v(0) = -wAsin(0) = 0...in other words, v(0) = 0...what am I missing here? I have an idea of where to go from here, but if someone could clarify how I'm supposed to start, that would be great. Thanks for your time.
     
  2. jcsd
  3. Apr 6, 2010 #2

    rock.freak667

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    Re: Oscillations - Finding Displacement at a Speed, Given Displacement at Another Spe

    Remember you have x=Acos(ωt+φ) so x(0) = Acosφ

    v=Aωsin(ωt+φ), v(0) does not give you Aωsin(0), remember there is still φ which is unaffected by t being equal to zero.
     
  4. Apr 7, 2010 #3
    Re: Oscillations - Finding Displacement at a Speed, Given Displacement at Another Spe

    Okay - not sure if this route even needs to be undertaken at all though...does this work?:

    Etotal = [tex]\frac{1}{2}[/tex]kx2 + [tex]\frac{1}{2}[/tex]mv2

    Etotal = 0 + [tex]\frac{1}{2}[/tex]0.1(2)2

    Etotal = 0.2

    0.2 = [tex]\frac{1}{2}[/tex](0.1)x2 + [tex]\frac{1}{2}[/tex]0.1(1)2

    x = 1.7

    Does that work?
     
  5. Apr 7, 2010 #4

    rock.freak667

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    Re: Oscillations - Finding Displacement at a Speed, Given Displacement at Another Spe

    Yes that works just as well.
     
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