How can Fourier analysis help find the spring constant (k)?

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Homework Help Overview

The discussion revolves around determining the spring constant (k) using data obtained from a spring system with a 0.5 kg weight. The data includes displacement in the x direction over time, and participants are exploring methods to analyze this data effectively.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss various methods to find the spring constant, including measuring extension with weights and using frequency data. Questions arise regarding the periodicity of the displacement data and its implications for analysis.

Discussion Status

Some participants have suggested using graphical analysis to determine the period of oscillation, while others propose conducting a Fourier analysis of the data. There is an acknowledgment of the limitations of the available data, and multiple approaches are being explored without a clear consensus on the best method.

Contextual Notes

Participants note that they are constrained by the data available, which consists solely of displacement as a function of time, and that further testing is not an option due to homework guidelines.

southport
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Using a program called tracker we have got data from a spring holding a 0.5 kg weight. We have the displacement in the x direction (positive x direction being down) and time. The task is to somehow find the spring constant (k) but I cannot for the love of me figure it out.
 
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Set the spring in a spring balance configuration and measure its extension for different weights. The slope of the distance vs weight graph is the spring constant. Units are force/distance.

See here http://en.wikipedia.org/wiki/Simple_harmonic_motion
 
Mentz114, this is a homework question and we don't have access to anymore testing, according to my teacher this is enough information.
 
What data do you have ? You need to know the frequency then you can use the formula ##f=(1/2\pi)\sqrt{k/M}##.
 
The only data we have is displacement as a function of time!
 
Does you displacement look periodic? Find the period.
 
southport said:
Using a program called tracker we have got data from a spring holding a 0.5 kg weight. We have the displacement in the x direction (positive x direction being down) and time. The task is to somehow find the spring constant (k) but I cannot for the love of me figure it out. Any help is greatly appreciated and this is urgent!
Plot a graph of the data, with time as the abscissa and displacement as the ordinate. From this graph, you should be able to visually tell what the period of the oscillation is. Assuming you know the relationship between the period and the frequency, you can then use Mentz114's formula to calculate the spring constant.
 
Do a Fourier analysis of the data !
 

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