- #1
Katy96
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Homework Statement
Homework Equations
The Attempt at a Solution
any help would be appreciated! I keep trying and just keep getting stuck really early on.
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Homework Help Overview
The discussion revolves around a physics problem involving a mass attached to a spring, focusing on the application of Newton's second law (ΣF = ma) and the implications of Hooke's Law. Participants are exploring the dynamics of the mass-spring system and the derivation of the governing differential equation.
Discussion Character
- Exploratory, Conceptual clarification, Problem interpretation, Assumption checking
Approaches and Questions Raised
- Participants express confusion about the initial steps in applying the relevant equations to the problem. There are inquiries into the forces acting on the mass and the implications of stretching the spring. Some participants attempt to clarify the relationship between force, mass, and acceleration.
Discussion Status
The discussion is ongoing, with participants sharing their understanding and questioning specific concepts. Guidance has been offered regarding the importance of drawing a free body diagram and labeling forces, but there is no explicit consensus on the next steps or a clear resolution yet.
Contextual Notes
Some participants indicate they are struggling with the foundational concepts and the application of equations, which may suggest a need for further clarification on the underlying physics principles.
any help would be appreciated! I keep trying and just keep getting stuck really early on.
- #2
SteamKing
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"getting stuck really early on" does not provide sufficient information to help you.
Please show what work you've done on this problem, or tell us what you don't understand about the question.
Please show what work you've done on this problem, or tell us what you don't understand about the question.
- #3
Katy96
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I don't understand where the first differential comes from
- #4
SteamKing
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I suppose you mean Equation 1?Katy96 said:
Do you know what ΣF = ma means?
- #5
Katy96
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yes force= mass*acceleration
- #6
SteamKing
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And how would you apply ΣF = ma to the problem with the mass and spring?Katy96 said:
- #7
Katy96
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that's where I get stuck
- #8
SteamKing
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Well, what forces are acting on the mass? If you assume the mass is at rest at point O, and you move it x-distance to the right, what happens to the spring? What does the displacement of the spring do to the mass?Katy96 said:
- #9
Katy96
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the spring is stretched so will want to go back to its original placeSteamKing said:
- #10
SteamKing
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Yes, but what does the tendency of the spring to unstretch itself do to the mass? What does it take to stretch the spring in the first place?Katy96 said:
- #11
Katy96
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it has to be stretched by something and to go back to its original it passes and oscillatesSteamKing said:
- #12
SteamKing
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What is this something? Do you know about Hooke's Law?Katy96 said:
https://en.wikipedia.org/wiki/Hooke's_law
- #13
Katy96
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yeah F=-kXSteamKing said:
- #14
SteamKing
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In your problem, you move the mass a distance x. What does that create in the spring? Make the mass a free body and label all the forces acting on it.Katy96 said:
- #15
TomW17
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First thing's first: you need to draw a good free body diagram. Label all the forces acting on the mass and their directions. The sum of these forces will be equal to the mass * the acceleration of the body (remember ##a(t) = \ddot{x}(t)##) , and the required DE will fall out pretty quickly from this.Katy96 said: