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Simple Harmonic Motion - Finding max speed of an oscillator

  1. Nov 29, 2008 #1
    1. The problem statement, all variables and given/known data
    A 300g oscillator has a speed of 95.4 cm/s when its displacement is 3.0 cm and 71.4 cm/s when it displacement is 6.0 cm. What is the oscillator's maximum speed?


    2. Relevant equations
    x = Acos([tex]\omega[/tex]t + [tex]\phi[/tex])
    v = -[tex]\omega[/tex]Asin([tex]\omega[/tex]t + [tex]\phi[/tex])
    vmax = [tex]\omega[/tex]A
    v = [tex]\omega[/tex](A^2 - x^2)^1/2

    3. The attempt at a solution
    I manipulated the fourth equation into

    [tex]\omega[/tex]A or vmax = (v^2 + (x[tex]\omega[/tex])^2)^1/2

    so if I get [tex]\omega[/tex] from somewhere else then I can use it to solve it for vmax but I can't see a way of doing that with the given info.
     
  2. jcsd
  3. Nov 29, 2008 #2
    Hmm... the fact that the mass is given gives me an idea. Try approaching the question from the conservation of energy, where Etot = 1/2 mv2 + 1/2 kx2. Equate Etot of the two cases would solve for k, and then one could find the value of Etot.

    The next step is fairly simple: at maximum speed, Etot = 1/2mvmax2
     
  4. Nov 29, 2008 #3
    Thank you very much for your help.

    For a value of k I got 44.48 N/m

    and for E[tex]_{}tot[/tex] I got about .157J

    and then solving for v[tex]_{}max[/tex] I got 1.022 m/s or 102.2 cm/s which makes sense.

    Thanks again for your help.

    KE0M
     
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