Spring Passing Equilibrium Position

AI Thread Summary
The discussion centers on determining how long a box of mass m remains in contact with a spring of spring constant k after sliding into it at speed v. Participants debate the correct formula for the contact time, with initial suggestions pointing to option A, which indicates a full oscillation duration. However, clarification reveals that the box is only in contact with the spring for half the period of oscillation, leading to the conclusion that the correct answer is actually related to pi. The key takeaway is that the box compresses the spring and then passes the equilibrium position, indicating a contact time of pi [m/k]½. Understanding the physics of oscillation is crucial for solving this problem accurately.
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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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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?
 
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?
 
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?
 
Oh, so wouldn't it just be pi?
 
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.
 

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