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Ideal Spring Question [Units]

  1. Oct 6, 2012 #1
    So, I'm trying to brush up on my undergrad physics, and I'm sure this is a bone-headed question, so please bear with me.

    1. The problem statement, all variables and given/known data
    A heavy object, when placed on a rubber pad that is to be used as a shock absorber, compresses the pad by 1cm. If the object is given a vertical tap, it will oscillate. Ignoring the damping, estimate the oscillation frequency. [The book i'm using actually gives the solution]


    2. Relevant equations
    x(t)=A*sin(sqrt(k/m)t+[itex]\phi[/itex])
    ω=sqrt(k/m)
    F=k|l-l0|

    3. The attempt at a solution
    We'll call x0 the equilibrium displacement, x0=1cm
    k=spring constant of rubber
    so
    k(l-l0)=k*x0=mg (equilibrium)
    gives us
    k=(mg)/(x0)
    then
    ω=sqrt(k/m)
    which eventually solves to
    ω=sqrt(g/x0)

    The book gives an answer of sqrt(980) rad/s. My question is given the units from ω=sqrt(g/x0) (meters, seconds, centimeters), how do they arrive at radians?
     
  2. jcsd
  3. Oct 6, 2012 #2

    ehild

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    Gold Member

    X0 is 0.01 m. So the unit of sqrt(g/x0) is 1/s.
    ω is the angular frequency, it is measured in radians/second, but radian is dimensionless. ω=2πf (f=frequency).

    ehild
     
  4. Oct 6, 2012 #3
    Makes sense. I actually just beefed the algebra cancelling my units. Thanks!
     
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