How Do You Calculate the Damping Constant of a Hard-Boiled Egg on a Spring?

[Punkyc7]

a 50 g Hard Boiled egg moves on the end of a spring with force constant k=25N/m. Its intial displacement is .3m. A damping force F=-bv acts on the egg and the amplitude of the motion decreases to .1 m in 5 sec. Calculate the magnitue of the damping contant b.

How exactly do you go about doing this?
I haven't been able to get anywhere on it.

 

[rickz02]

Start with the solution of the equation of motion for this system.

 

[Punkyc7]

so we have

x=Ae^-(b/2m)t cos(w't+phi)

where w'=(k/m -b^2/4m^2)^1/2

so here's the problem do you use the initial conditions to solve for b or the final positions, does it make a difference?

 

[rickz02]

Before you can solve for b you have to apply the initial conditions to solve for A beforehand. Just assume phi is 0.

Once you have the value for A, solve for b using the other informations given (btw, don't assume that those are for the final position).

 

[Punkyc7]

isnt A=.3 since that's the starting position
i put it into a function solver and i got
2.94587866888,

does that seem right?

also i didnt use the .1 if i was suppose too

 

[rickz02]

Lol...I advise you to analytically or numerically solve this problem as I doubt your teacher would accept your answer. I admit solving for b is a bit tedious but you already got A! Keep on working...

Also usually 0\leq b\leq 1.

Hint: Work with the amplitude of oscillation component of your equation instead of working with the whole thing.

 

[Punkyc7]

ok so ignoring the cos stuff i got

.2197224577

is this one right?

its in the interval