# Hard Boiled egg on a spring

1. Jun 23, 2011

### 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 havent been able to get anywhere on it.

2. Jun 24, 2011

### rickz02

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

3. Jun 24, 2011

### Punkyc7

so we have

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

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

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

4. Jun 24, 2011

### 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, dont assume that those are for the final position).

5. Jun 25, 2011

### Punkyc7

isnt A=.3 since thats 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

6. Jun 25, 2011

### 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.

7. Jun 25, 2011

### Punkyc7

ok so ignoring the cos stuff i got

.2197224577

is this one right?

its in the interval