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Damped Harmonic Motion

  1. Feb 23, 2008 #1
    1. The problem statement, all variables and given/known data

    Hi all,

    A hard boiled egg, with a mass m=51g, moves on the end of a spring, with force constant k=26N/m. It's initial displacement is 0.300m. A damping force F[tex]^{}x[/tex]=-bv[tex]^{}x[/tex] acts on the egg and the amplitude of the motion decreases to 0.106m in a time of 5.45s.

    Calculate the magnitude of the damping constant b.

    2. Relevant equations

    (1) [tex]\omega[/tex]'=[tex]\sqrt{k/m-(b/2m)^2}[/tex] where [tex]\omega[/tex]' is the damped angular frequency

    (2) x(t)=Ae^(-bt/2m)cos([tex]\omega[/tex]'t) where x(t)=displacement, A=amplitude, t=time, e=natural exponential, w'=as above.

    3. The attempt at a solution

    I cannot see how you can calculate the damping constant from the data given. Equation (1) above has two unknowns w' and b, while equation (2) has three x(t), b and w'.

    I tried to rearrange equation (2) to get w' as the subject, but found I was unable to separate the variables. I also attempted setting w' as equal to [tex]\sqrt{k/m}[/tex], but this gave the wrong answer too. I'm really just stabbing in the dark, so some help to understand how to go about it is what I need.

    I must be missing something obvious and fundamental, for instance is there another way you can calculate [tex]\omega[/tex]' from the given data?

    Please help!
     
    Last edited: Feb 24, 2008
  2. jcsd
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