Finding the Damping Constant for a Hard-Boiled Egg on a Spring

[TFM]

Homework Statement

A hard-boiled egg of mass 51.0kg moves on the end of a spring with force constant 25.7N/m. Its initial displacement is 0.293m. A damping force f (x) = -bv (x) acts on the egg, and the amplitude of the motion decreases to 0.101m in a time of 4.55s.

Calculate the magnitude of the damping constant .

Homework Equations

f (x) = -bv (x)

curly:} w'=sqrt(k/m - b^2/4m^2)

The Attempt at a Solution

I used:

f (x) = -bv (x)

rearranged to give:

b = -f/v (x)

but this didn't work

Do I have to use:

curly:} w'=sqrt(k/m - b^2/4m^2)

and if so, what's the best way to calculate angular frequency (curly:} w')?

TFM

 

[TFM]

Any Ideas...?

 

[HallsofIvy]

You have "w'=sqrt(k/m - b^2/4m^2)"

I can assume that m is the mass of 51 kg (are you sure you copied that right?) and b is the damping coefficient you want to find. I can even guess that k is the spring constant 25.7 N/m but unless you tell what w' means, that equation is meaningless.

 

[TFM]

It sthe curly Greek w', which I believe means Angular Frequency (?)

TFM

 

[TFM]

Are yes, the egg is 51g

TFM

 

[TFM]

I have rearranged the equation to get:

b^2 = 4m^2*((k/m)-(w'^2))

I just need to work out angular frequency from the given infomration, but I am not sure what to do...

TFM

 

[TFM]

Any Ideas?

TFM

 

[TFM]

w' is the Greek letter (small) omega with a ' . It says that the angular frequency w' is given by:

sqrt(k/m - b^2/4m^2)

But I thought that when a letter has a ' by it, you have to differntiate it?

Can anyone give me sime ideas about what formula's are suitable to find the angular frequency, given the above initial data?

TFM