Spring Passing Equilibrium Position

In summary: This can be represented by tcontact = 1/2π√(m/k). So in summary, the box is in contact with the spring for half the period of a full oscillation, which can be represented by tcontact = 1/2π√(m/k).
  • #1
TwinGemini14
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http://i662.photobucket.com/albums/uu347/TwinGemini14/showme2.gif

A box of mass m slides at an initial speed v into a relaxed spring of spring constant k.

How long is the box in contact with the spring before it passes the equilibrium position again?

A) tcontact = 2p [k/m]½
B) tcontact = p [m/k]½
C) tcontact = ½ p [m/k]½

p here represents pi.

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I believe the correct answer is A, because the box is with contact will the spring for a full oscillation. So 2pi.

Can somebody help me on this one, I seem to be really stuck. Thanks in advance!

(I posted a link to a picture of the system on the top.)
 
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  • #2
TwinGemini14 said:
I believe the correct answer is A, because the box is with contact will the spring for a full oscillation.
Why do you think it's in contact for a full oscillation? What would represent a full oscillation?
 
  • #3
I just assumed that when the block hits the spring, it compresses it and then the spring restores back to its equilibrium position, thus releasing the block then. In that case, it travels one complete oscillation. That was my assumption. Can somebody please explain the physics behind this problem?
 
  • #4
TwinGemini14 said:
I just assumed that when the block hits the spring, it compresses it and then the spring restores back to its equilibrium position, thus releasing the block then. In that case, it travels one complete oscillation.
When a mass at the end of spring oscillates, it goes from one extreme to the other on each side of the equilibrium point. Here you start at equilibrium, go to full compression (one extreme), then pass the equilibrium point. What would be next for a full oscillation?
 
  • #5
Oh, so wouldn't it just be pi?
 
  • #6
TwinGemini14 said:
Oh, so wouldn't it just be pi?
The box is in contact with the spring for half the period of a full oscillation.
 

FAQ: Spring Passing Equilibrium Position

1. What is the "Spring Passing Equilibrium Position"?

The Spring Passing Equilibrium Position is the point at which a spring, when displaced from its resting position, has passed through its equilibrium point and is moving towards its maximum displacement.

2. How does the "Spring Passing Equilibrium Position" relate to the concept of equilibrium?

The Spring Passing Equilibrium Position is an important concept in understanding the equilibrium of a spring. It is the point where the forces acting on the spring are balanced, meaning the spring is neither compressed nor stretched. Beyond this point, the spring will continue to move until it reaches its maximum displacement, at which point the forces will be balanced again.

3. What factors can affect the "Spring Passing Equilibrium Position"?

The Spring Passing Equilibrium Position can be affected by various factors, including the initial displacement of the spring, the mass of the object attached to the spring, and the stiffness of the spring itself. Additionally, external factors such as air resistance and friction can also have an impact on the spring's movement.

4. Can the "Spring Passing Equilibrium Position" be calculated?

Yes, the Spring Passing Equilibrium Position can be calculated using the formula x = A cos(ωt + φ), where x is the displacement from the equilibrium position, A is the amplitude of the spring's oscillation, ω is the angular frequency, and φ is the phase shift. However, this calculation may become more complex if external factors are involved.

5. How is the "Spring Passing Equilibrium Position" used in real-world applications?

The concept of the Spring Passing Equilibrium Position is used in various real-world applications, such as in the design of suspension systems for vehicles, shock absorbers, and even musical instruments. It is also an important concept in understanding the behavior of waves, and is used in fields such as seismology and acoustics.

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