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ODE application of damped motion

  1. Mar 24, 2013 #1
    1. The problem statement, all variables and given/known data
    A mass of 40 g stretches a spring 10 cm. A damping device imparts a resistance to motion numerically equal to 560 (measured in dynes/(cm/s)) times the instantaneous velocity. Find the equation of motion if the mass is released from the equilibrium position with a downward velocity of 2 cm/s.


    2. Relevant equations

    [itex]\frac{d^2x}{dt^2}+\frac{β}{m}\frac{dx}{dt}+\frac{k}{m}x=0[/itex]

    3. The attempt at a solution
    The only thing I think that's stopping me from doing this problem is the units. I converted 40g to .04 kg, and 10 cm to 0.1 m. But I'm not sure what to do with the 560 dynes/(cm/s). Do I turn that into 56000 dynes/(m/s)? That seems like a huge number for β, considering I used 0.4 in the last problem for β.
    Thanks.
     
  2. jcsd
  3. Mar 24, 2013 #2
    In principle, you do not have to convert any units, all the given values are consistently in CGS.

    But if you want to, then the resistance is indeed 56000 dynes per m/s, but you need to finish the conversion to newtons per m/s.
     
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