Trying to Calculate k, using Hooke's Law

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Homework Help Overview

The problem involves calculating the spring constant \( k \) using Hooke's Law in the context of an oscillating mass. The position of the mass is described by a cosine function, and the participant is attempting to relate this to the spring constant.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to apply the formula \( k = mg/x \) based on given parameters but questions the correctness of their calculations. Other participants suggest reconsidering the relationship between the oscillation amplitude and the spring constant, and they highlight the importance of understanding the equilibrium state of the spring.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem. Some guidance has been offered regarding the relationship between the spring's stretch and the oscillation, but there is no explicit consensus on how to proceed with the calculations.

Contextual Notes

Participants note the lack of information regarding the spring's initial length and the context of the oscillation (e.g., whether it is vertical or horizontal), which affects the application of the equations involved.

masterexploder
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Homework Statement


The position of a 49 g oscillating mass is given by x(t)=(1.8cm)cos12t, where t is in seconds.

Homework Equations


k=mg/x

The Attempt at a Solution


I've tried working this problem multiple different ways and it is just not working for me.
I used k= (.049*9.8)/.018
Is this correct with the information I've been given? I used up all my attempts and the solution is apparently
7.1 N/m...but I keep coming up with roughly 26.7 N/m
 
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Hello ex master, :welcome:
masterexploder said:
Is this correct with the information I've been given
It is not. One can stretch a spring wrt its equilibrium state, and then let go. The amount of stretch becomes the amplitude of the ensuing oscillation so it has little to do with the spring constant.
You have been given another bit of info that does have a relationship with the spring constant. Can you guess which bit ?
 
kx = mg answers the question "how much does the spring stretch when I add this mass". It is an equilibrium answer. The problem didn't tell you how long the spring was before you added mass, or for that matter how long the spring was after the mass was added. What you have is how the spring oscillates about the equilibrium point. Do you have any other equations or ideas that might apply?
 
Cutter Ketch said:
kx = mg answers the question "how much does the spring stretch when I add this mass
Yes, but even then that is only in a vertical context.
@masterexploder , there is nothing in the question about the spring being vertical. This could be happening on a smooth horizontal surface, so you have no basis for involving g.
 
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