Calculate Damping Coefficient of 50.0g Egg

In summary, a 50.0-g hard-boiled egg moves on the end of a spring with force constant . It is released with an amplitude 0.300 m. A damping force acts on the egg. After it oscillates for 5.00 s, the amplitude of the motion has decreased to 0.100 m.Calculate the magnitude of the damping coefficient . Express the magnitude of the damping coefficient numerically in kilograms per second, to three significant figures.
  • #1
mlee
24
0
A 50.0-g hard-boiled egg moves on the end of a spring with force constant . It is released with an amplitude 0.300 m. A damping force acts on the egg. After it oscillates for 5.00 s, the amplitude of the motion has decreased to 0.100 m.Calculate the magnitude of the damping coefficient . Express the magnitude of the damping coefficient numerically in kilograms per second, to three significant figures

pls who can help me?
thanx
 
Physics news on Phys.org
  • #2
How should Newton's 2.law of motion look like?
 
  • #3
i think it is:
-kx-bv=ma
 
  • #4
That's correct!
Now, what type of solutions have you learned that this differential equation has?
 
  • #5
See it as

[tex] -kx - b \frac{dx}{dt} = m\frac{d^2 x}{dt^2} [/tex]
 
Last edited:
  • #6
You're right, thanks alridno :smile:
 
  • #7
v= dx/dt and a= d^2/dt^2
 
  • #8
but what is the answer of d^2/dt^2 then?
 
  • #9
mlee:
Any progress at what sort of solutions your equation has?
 
  • #10
uh not really...;(
 
  • #11
Now, I'd like you try a solution of the form:
[tex]x(t)=Ae^{rt}[/tex] (A and r constants)
What condition must be placed on "r" in order for this to be a solution.
Please post your work.
 
  • #12
Asin(wt)+Bcos (wt)
 
  • #13
mlee said:
Asin(wt)+Bcos (wt)
This is a solution of an UNDAMPED, harmonic oscillator.
Your oscillator is NOT undamped; try my approach, and post your work.
 
  • #14
Ae-bt/2mCos(ω't + φ)
 
  • #15
Ae^(bt/2m)*cos(w't+φ)
 
  • #16
You lack a minus sign in your exponential!
Now, knowing
a) The initial displacement
and
b)That the initial velocity is zero
How can you determine [tex]A,\phi[/tex]

Besides, what is your value of "w"?
 
  • #17
ω = sqrt(k/m)
ω' = √((k/m) - (b²/4m²))
 
  • #18
Now, so how does your initial conditions determine [tex]A,\phi[/tex]?
 
  • #19
i don't know how to find [tex]phi[/tex]
 
  • #20
and w' = 5*10^2-(b^2/1*10^-2)
is that right?
 
  • #21
Now, initially we have:
[tex]A\cos\phi=A_{0}[/tex]
where [tex]A_{0}[/tex] is the initial displacement.
In order to find the position, we differentiate:
[tex]\frac{dx}{dt}=Ae^{-\frac{bt}{2m}}(-w'\sin(w't+\phi)-\frac{b}{2m}\cos(w't+\phi))[/tex]
Hence, for t=0, we must have:
[tex]0=A(-w'\sin(\phi)-\frac{b}{2m}\cos(\phi))[/tex]
 
  • #22
Furthermore, in order to solve the problem, remember that:
[tex]Ae^{\frac{-bt}{2m}}[/tex] is the AMPLITUDE as a function of time..
 
  • #23
cos phi is 0.333?
is that right?
 
  • #24
You get the equations:
[tex]A\cos\phi=A_{0}[/tex]
and
[tex]tan\phi=-\frac{b}{2mw'}[/tex]
 
  • #25
b is unknown
 
  • #26
You're right!
While I have a method to determine 'b', I don't think this is what has been intended.
I think that it has been assumed (incorrectly!) that the amplitude function is:
[tex]A_{0}e^{\frac{-bt}{2m}}[/tex]
where [tex]A_{0},m[/tex] are known quantities.
Hence, it is simple to determine 'b' from this.
(Just plug in the proper t-value and set your amplitude equal to the given value)
I think this has been the intention; the equation you may derive for 'b' is not easy to solve.
 

1. How do you calculate the damping coefficient of a 50.0g egg?

The damping coefficient of an object can be calculated by dividing the natural logarithm of the amplitude ratio by the period of oscillation. In the case of a 50.0g egg, the damping coefficient can be determined by measuring the amplitude of its oscillation and the time it takes to complete one full cycle of oscillation.

2. What is the significance of calculating the damping coefficient of an egg?

The damping coefficient of an object, in this case an egg, can provide information about its internal structure and the forces acting upon it. It can also help in predicting the behavior of the object under different conditions, such as changes in temperature or external forces.

3. Can the damping coefficient of an egg change over time?

Yes, the damping coefficient of an egg can change over time due to various factors such as changes in its environment, physical damage, or structural changes. It is important to regularly measure and monitor the damping coefficient to track any changes in the behavior of the egg.

4. How does the damping coefficient affect the stability of an egg?

The damping coefficient is a measure of the egg's ability to resist oscillation and maintain its position. A higher damping coefficient means the egg is more stable and less likely to topple over. On the other hand, a lower damping coefficient indicates a less stable egg that is more susceptible to external forces.

5. Is there a standard damping coefficient for a 50.0g egg?

No, the damping coefficient of an egg can vary depending on its size, shape, and physical properties. It is important to calculate the damping coefficient for each individual egg to accurately assess its stability and behavior.

Similar threads

  • Introductory Physics Homework Help
Replies
17
Views
277
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
2
Views
10K
  • Introductory Physics Homework Help
Replies
3
Views
1K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
871
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
Replies
6
Views
6K
  • Introductory Physics Homework Help
Replies
6
Views
2K
  • Introductory Physics Homework Help
Replies
3
Views
3K
Back
Top