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As we all know, force applied to a spring is directly proportional to the extension of spring as shown below:

enter image description here

However, my experimental results for a simple spring from a school laboratory don't match this behaviour:

enter image description hereenter image description here

Why is this happening? I don't think systematic error is the reason that is causing the experimental graph to move away from the origin.

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  • $\begingroup$ With no applied force, are all the coils of the spring equally spaced? Do they remain equally spaced when the force is between 0.5 and 1.5 N? $\endgroup$ – Bob D Jan 18 at 4:19
  • $\begingroup$ Also, what means are you using to fix one end of the spring in place? $\endgroup$ – Bob D Jan 18 at 4:24
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    $\begingroup$ Perhaps the experiment is done vertically where the effect of gravity shifts the equilibrium? So at zero displacement, gravitational force acts? And this will remain constant throughout the experiment considering small displacements. This will come as a shift in y axis. $\endgroup$ – Fellow Traveller Jan 18 at 4:32
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    $\begingroup$ Actually a teaching moment that tells you that actual physical systems behave according to the platonic/mathematical ideal only with certain ranges. Once properties of the material start to be considered, it's not linear. In this case, you can also stretch the spring to breaking point and plot. It's not gonna be linear up there either. $\endgroup$ – David Tonhofer Jan 18 at 17:37
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    $\begingroup$ Please note that you didn't really give us a description of what experiment you're doing here. You're lucky that many physicists will be able to guess what you're doing, but when you're asking a question about experimental results, please always include a detailed enough description of what exactly you're doing so that people don't have to guess! $\endgroup$ – ACuriousMind Jan 19 at 19:32
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The coils of the spring are touching one another and the spring is initially under self-compression so it takes a finite force to move all the coils away from one another and for the spring to behave as you expected.
That initial part of the source vs stretch curve is real (you had obtained data whilst undertaking an experiment) and hence should not be ignored.

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    $\begingroup$ This is supported by articles in The Physics Teacher 1980 and 2019 $\endgroup$ – jkien Jan 18 at 12:33
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There is no "systematic error" in the experimental results. I have done this experiment as well when teaching a high school physics class. The effect you are seeing is due to the fact that the spring you are using requires a small amount of force before it begins to stretch, while the "theoretical" spring that is described by Hooke's Law does not. This effect for your real-world spring is real, and may be due to heat treatment or other handling of the spring material when it was coiled into the spring shape upon manufacture.

Note that you should not assume that the graphed data should be curved downward in order to force the graph through the origin, as this is not what you measured.

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  • $\begingroup$ Could you please explain more about the factor/reason that cause the effect that I saw? Tqvm $\endgroup$ – James Tan Jan 18 at 7:35
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    $\begingroup$ As Farcher pointed out, the spring is under self-compression. I'm not a metallurgist so I don't know the exact reason for this, but my guess is that the spring was heat treated and wasn't "compressed" when it was hot, but it became compressed as it cooled to room temperature, due to thermal contraction. $\endgroup$ – David White Jan 18 at 16:42

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