Finding spring constant from a graph

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Discussion Overview

The discussion revolves around the possibility of determining the spring constant from force/time and position/time graphs in the context of a mass oscillating on a spring. Participants explore the relationship between the spring constant and various measurements, including gravitational potential energy and oscillation frequency.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions whether the spring constant can be derived from the equation mgh = 1/2kx^2 using the provided graphs.
  • Another participant suggests writing a function for x(t) and inquires about the presence of the spring constant k in that expression, relating it to a specific time interval.
  • A third participant recommends drawing a free body diagram and performing a force balance to analyze the situation further.
  • Another participant emphasizes the need for clarity regarding whether the oscillation is part of an experiment or an observation and discusses the method of calculating the spring constant using the frequency of oscillation.
  • There is a suggestion that the question about deriving k from the graphs is vague and seeks clarification on the source of the data.

Areas of Agreement / Disagreement

Participants express differing views on the clarity and methodology of finding the spring constant, indicating that the discussion remains unresolved with multiple competing approaches and interpretations.

Contextual Notes

Participants have not reached a consensus on the method to find the spring constant, and there are unresolved questions about the nature of the measurements and the accuracy required.

John Sena
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Assume a spring with a mass attached is oscillating.
Can i find spring constant from force/time and position/time graph using mgh=1/2kx^2?
The force in force/time graph is collected from force meter attached at the top of the spring.
The positin in position/time graph is the distance of the mass from the ground.
 
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John Sena said:
Assume a spring with a mass attached is oscillating.
Can i find spring constant from force/time and position/time graph using mgh=1/2kx^2?
The force in force/time graph is collected from force meter attached at the top of the spring.
The positin in position/time graph is the distance of the mass from the ground.

If you write a function for x(t) what do you get? x(t) = x(t=0) + ... Does this expression have k anywhere? How does this relate to an important time interval?
 
Draw a free body diagram for the mass, and write a force balance for the mass. What do you get?

Chet
 
John Sena said:
Assume a spring with a mass attached is oscillating.
Can i find spring constant from force/time and position/time graph using mgh=1/2kx^2?
The force in force/time graph is collected from force meter attached at the top of the spring.
The positin in position/time graph is the distance of the mass from the ground.

There is something not quite clear here and it requires a bit more explanation.

First of all, is this something that is part of a measurement or experiment? Are you simply given a spring with a mass, and it is ALREADY oscillating? How accurate do you need this to be?

You see, if this is simply an experiment or an observation, you can easily calculate the spring constant by simply measuring the frequency of oscillation. Measure how many times the mass makes a complete oscillation in one second, and you have the frequency of oscillation. Then simply use the fact that for a SHO system,

f = (1/2pi)*(sqr(k/m)

Knowing the mass, you immediately get the value of k.

Asking if you can find the spring constant from the force-time or position-time graph is vague. Were you GIVEN these or were you asked to measure these?

Zz.
 

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