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Measuring spring constant using oscilations of a mass.

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The aim of this experiment is to use oscillations of a mass on a spring to the find the spring constant, k and the effective mass of the spring. The reason to carry out this experiment is to find the value of the effective mass, me and to see if it is small enough to be ignored as some teachers think or not.


  • Spring
  • Weights
  • Stopwatch
  • Retord Stand
  • Clamp
  • Table

Apparatus Specification


Range Of Measurement

Maximum Measurement

Minimum Measurement


0.100Kg – 0.600Kg




0.01 sec – 356400.00 sec

356400.00 sec

0.01 sec


The apparatus will be set up as shown in the diagram.

The Retord stand and the clamp are going to be used to hang the spring a certain height above the surface of the table. The masses are going to be kept nearby along with the stopwatch to measure the oscillations. Initially the time will be recorded for 0.100Kg. The spring would be given a reasonable vertical displacement for which the time would be recorded. Which is the time for 20 oscillations. The time recorded would be for 20 oscillations. This experiment is then repeated for the same weight three times and then for the rest of the weights up to 0.600Kg. The reason to carry out the experiment three different times for the same mass is to get a reasonable average. The times will be recorded in the results table, a graph would be drawn and the values of k and me

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Preliminary Graph

The graph of the preliminary results is done on the next page

If I use the results that I got and my graph the preliminary values that I get for k and me are as follows:

k        =        4 π2 / M

k         =        4 π2 / 1.373        

k        =        28.75

If I use this value of k my preliminary value for mewould be:

me        =        C  x  k / 4 π2

me        =        0.0125 x 28.77 / 4 π2

me        =        0.00910 kg

My preliminary results come up with the value for k of 28.75 and value of me, which is 0.00910 kg.

The worked out value for k is quite different to the value that was obtained by the force/extension data. The value of effective mass, meisn’t that different to the real value. The actual values of k and me, are 23.88 and 0.00900 kg respectively.

The difference between these values could be due to the following reasons among with others:

  • I couldn’t measure the time properly for the oscillations meaning that I took more time to react after I saw the spring go above or below the fiducial marker.
  • It could also be because the mass added on the spring could have been a little different (e.g. 0.605Kg instead of 0.600kg) then mentioned on the mass itself.

While I am working for my real results I would have to careful about avoiding these mistakes or these reasons for errors as much as I can so that the value I get for k and meare more accurate.


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Using more then thirty periods for the heights might not have been that accurate due to it taking more time and the increased number might result in losing count.

Less then thirty periods would insure that this technique could be applied in practise but would not be sufficient to form a reliable conclusion and analysis upon.

Comment On Reliability Of Conclusion

According to the analysis and the calculations made my conclusion would be reliable in the sense that the calculated value of g is quite good and accurate to the actual value of g meanwhile the calculated value of h is a bit far from the actual and predicted value. The percentage error in the actual value of h is 3.30%, meanwhile the percentage error of g is 3.25%.

This means that the conclusion is reliable more in favour of g than in h.

Future Improvements Or Further Work

As suggested earlier if the technique of the experiment was to be improved using an electronic timing device that is connected to a computer, so it can also help to plot the graphs.  This method would avoid any additional time taken by the human and avoid any systematic error to quite an extent.

A second improvement could be that the for the height something suitable like a Vernier calliper or more then one set square be used to make sure that the height if the pendulum is accurate.

Cable Trunking Experiment                -  –

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