Damped Harmonic Motion

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Homework Statement



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.

Homework 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.

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:

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