Question Interpretation: "Describe the energy conversions in spring"

[Jaimie]

Homework Statement

Hi,
I have a question in interpreting the following question:
"Describe the energy conversions in a spring undergoing simple harmonic motion as it moves from the point of maximum compression to maximum stretch in a frictionless environment. Be sure to point out the points at which there will be...
i) maximum speed
ii) minimum speed
iii) minimum acceleration"

I know how to explain the motion and the answers for this but I'm wondering if the question is asking about simple harmonic motion for a vertically hanging spring (vertical motion, no friction) or simple harmonic motion for a wall-attached spring (horizontal motion, no friction) as it compresses and expands on a table surface? I understand that both scenarios involve simple harmonic motion without friction. In this chapter we are looking simple harmonic motion of a spring with no friction.

Thank you for your time.

Homework Equations

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The Attempt at a Solution

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[NascentOxygen]

I would think either case would see you earn full marks if explained correctly, but since you ask I'd say go with the latter.

 

[CWatters]

The question asks about the energy conversions involved. In both cases the energy conversions that they are likely to be most interested in are similar (although not identical). I agree with NascentOxygen, the latter (horizontal case) is simpler.

 

[olivermsun]

I think the energy conversions should be the same, no matter which case you choose to describe. I agree with NascentOxygen that it shouldn't matter as long as you make it clear what you are explaining and explain it correctly.

 

[HalfLostAndSearching]

I would interpret the question as asking about the energy conversions in a spring undergoing simple harmonic motion in a frictionless environment, regardless of whether it is a vertically hanging spring or a wall-attached spring. In both scenarios, the spring would experience the same energy conversions as it moves from maximum compression to maximum stretch. These energy conversions involve the interplay between potential energy and kinetic energy.

At the point of maximum compression, the spring has the maximum potential energy and zero kinetic energy. As the spring begins to stretch, the potential energy decreases and the kinetic energy increases. This continues until the spring reaches its equilibrium position, where the potential energy is at its minimum and the kinetic energy is at its maximum. This is the point of maximum speed.

As the spring continues to stretch, the kinetic energy decreases and the potential energy increases until the spring reaches its maximum stretch, where the potential energy is at its maximum and the kinetic energy is at its minimum. This is the point of minimum speed.

At both the points of maximum speed and minimum speed, the acceleration of the spring is zero. This is because the spring is momentarily at rest before changing direction.

In summary, the energy conversions in a spring undergoing simple harmonic motion involve the conversion of potential energy to kinetic energy and vice versa, with the points of maximum speed, minimum speed, and minimum acceleration occurring at specific points in the motion. These conversions occur in both a vertically hanging spring and a wall-attached spring, as long as there is no friction present.