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I measured the periodic movement of a spring with a mass and plotted it

enter image description here

enter image description here

Looking at the first graph, I assumed the frequency is somewhere between 2-2.5 Hz.

The mass hanged on spring was 100 g. Using the second plot I estimated the spring constant to be about 3 Nm$^{-1}$. Now using the formula $$f=\frac{1}{2\pi}\sqrt{\frac{k}{m}}$$ plugging in the numbers I get a frequency value of about 0.87 Hz, which is not even close to the one that can be seen on the first plot.

I've been sitting at this for a few hours now. I've asked my partner, neither of us can determine what's the problem. I thought it might be neglecting the spring's mass, but fixing that would only make the theoretical frequency lower. Can anybody help me?

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    $\begingroup$ You sure about the mass $m = 100\,\text{g}$? For $m=10\,\text{g}$ you get the desired frequency. $\endgroup$ – AlmostClueless Jun 2 at 12:10
  • $\begingroup$ 100% sure, I've held it my hand, there was a label saying 100g and we put it on a scale to be sure. $\endgroup$ – Dio Jun 2 at 12:17
  • $\begingroup$ Is the force-sensor calibrated appropriately? Did you measure the weight of the mass with the force sensor? $\endgroup$ – robphy Jun 2 at 13:20
  • $\begingroup$ What brand of equipment are you using? Is it rated for giving reliable results with such small forces? $\endgroup$ – Bill N Jun 2 at 14:46
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It sounds like a sensor/software discrepancy to me. It also appears that you zeroed the force sensor with the mass at equilibrium position. That's okay, but it hides whether the force sensor was reading correctly. Also, was there a mass hanger (usually 50 g) that you placed your 100 g mass on.

I don't know how you measured the distance of travel, but be sure of the following:

  1. Calibrate your force sensor and position sensor.
  2. Be sure that any sensitivity settings on the sensors (1X, 10X, 100X switches) are on 1X, or that you compensate the measurement for other settings.
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On the force axis on the second plot, the numbers are quite small, did you use $F=mg$ to convert masses to Newtons before plotting? Perhaps that needs doing.

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  • $\begingroup$ The plot looks like the output of a force sensor attached to the spring. I doubt that a mass-to-weight conversion is needed. $\endgroup$ – Bill N Jun 2 at 14:16
  • $\begingroup$ maybe, but as AlmostClueless also noticed, increasing k by a factor 10, makes things much closer $\endgroup$ – John Hunter Jun 2 at 14:19
  • $\begingroup$ so maybe the force sensor is reading in kg $\endgroup$ – John Hunter Jun 2 at 14:27
  • $\begingroup$ In both the PASCO and Venier software, the force sensor readings are plotted in newtons unless there is deliberate user intervention. In those cases, the software automatically changes the units on the plot. $\endgroup$ – Bill N Jun 2 at 14:29
  • $\begingroup$ Sometime there is a sensitivity control with 1X, 10X, 100X settings on the sensor itself. If that wasn't on 1X, that could explain it. $\endgroup$ – Bill N Jun 2 at 14:30

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