# Damped Harmonic Motion

## 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$$^{}x$$=-bv$$^{}x$$ 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) $$\omega$$'=$$\sqrt{k/m-(b/2m)^2}$$ where $$\omega$$' is the damped angular frequency

(2) x(t)=Ae^(-bt/2m)cos($$\omega$$'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 $$\sqrt{k/m}$$, 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 $$\omega$$' from the given data?

Please help!

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