Hard Boiled egg on a spring

In summary, the magnitude of the damping constant for a 50 g hard boiled egg moving on the end of a spring with force constant k=25N/m and initial displacement of .3m is .2197224577, based on the given information of a damping force F=-bv and the amplitude of motion decreasing to .1m in 5 seconds. This is obtained by solving the equation of motion for the system and using the initial conditions to solve for the amplitude A and then solving for b using the amplitude of oscillation component of the equation. The resulting value should be in the range of 0 to 1.
  • #1
Punkyc7
420
0
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.
 
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  • #2
Start with the solution of the equation of motion for this system.
 
  • #3
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?
 
  • #4
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).
 
  • #5
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
 
  • #6
:smile: 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 [itex]0\leq b\leq 1[/itex].

Hint: Work with the amplitude of oscillation component of your equation instead of working with the whole thing.
 
  • #7
ok so ignoring the cos stuff i got

.2197224577

is this one right?

its in the interval
 

1. How does a hard boiled egg balance on a spring?

The yolk and white of a hard boiled egg are solid and dense, making the center of gravity lower and easier to balance on a small surface like a spring.

2. Can you crack a hard boiled egg on a spring?

Yes, it is possible to crack a hard boiled egg on a spring if enough force is applied. However, the solid structure of the egg makes it more difficult to crack compared to a raw egg.

3. How does the spring affect the texture of the egg?

The spring does not have a significant effect on the texture of a hard boiled egg. The egg remains solid and intact, with no changes in texture.

4. Is it safe to eat a hard boiled egg that has been on a spring?

As long as the egg was properly cooked and handled before being placed on the spring, it should be safe to eat. However, it is not recommended to eat food that has been in contact with non-food objects like a spring.

5. Can a raw egg also balance on a spring?

No, a raw egg will not balance on a spring due to its liquid contents. The raw egg's center of gravity is higher, making it more difficult to balance on a small surface like a spring.

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