# Finding the Spring Constant

One example of simple harmonic motion is the oscillation of a mass on a spring. The period of oscillation depends on the spring constant of the spring and the mass that is oscillating. The equation for the period, T, where m is the suspended mass, and k is the spring constant is given as We will use this relationship to find the spring constant of the spring and compare it to the spring constant found using Hooke’s Law. Referring back to the data we collected, we can conclude from it that the speed of the spring decreases as more mass is place on the string; hence the time it takes to complete ten oscillations is more.

When a mass is put on a spring, it doesn’t stay in just one place as it keeps moving and exceeding its equilibrium point every time. This is recognized as SHM (simple harmonic motion) as no other frictional forces are causing disturbance. I guess from our final result to be fairly accurate (since we obtained 25.

980i?? 4. 049 and the theoretical value was 28. 701i?? 4. 007 N/m which we got from our previous lab where we had to find the spring constant), we can conclude that there was slightly little damping (where there is a change in amplitude) however there was damping since our final result wasn’t that close to the theoretical.

When more mass is put on a string, it is obvious that the spring will not have much motion as there is being more and more force put on it.

Since the mass keeps its force on the spring, it takes the spring a lot more time to complete an oscillation. The spring however cannot be indestructible because there is a certain limit of the spring where it cannot extend any further. When a mass exceeds a spring’s limit, the spring beings to deform and this at one point due to an incredible amount of force, the spring breaks.

Note- The y-intercept was zero as the line stretched out went through the zero point. This tells us that our results were very good as we obtained a well straight line. We can comment on the correlation as well where we can state it was quite accurate as the Ri?? value was 0. 997 which indicates a good correlation in the graph. We can also see from the graph how the correlation is a strong positive correlation. If we look at the graph, we are able to identify a strong positive correlation between the time it takes to complete ten whole oscillations and the mass placed on the spring..

We can determine that there weren’t that many errors since the R-squared value displayed on the graph is nearly 1, we can see how errors were at its minimum. There were however some errors since the experimental value wasn’t exactly the same as the theoretical value (which was 28. 701i?? 4. 007 N/m –> this was gotten from our previous lab where we had to find the spring constant) as it was just a bit off. Since the two values are positively correlated, the time is proportional to the mass (Ti??? m), thus this illustrates that the spring takes quite a long time to complete one whole oscillation.

The spring wasn’t really that well clamped to the standing clamp and the loose ends might have caused the spring constant value to be far greater that what it is supposed to be. This systematic error may surely have altered the uncertainty value as it could have either increased it or decreased it. This could have easily caused inaccuracy since the uncertainties wouldn’t be calculated correctly like they were supposed to. To improve this, we should tie a string round the spring we are using so that it is properly attached to the standing clamp and so that the spring constant decreases.

Weakness: Reaction time is a minor weakness in this experiment. Before letting go of the mass placed on the string, the timer was already started which illustrated the inaccuracy present in our results. It goes the other way around as well because at the time the 10 oscillations come to an end, the time recorded when the oscillations finished might also been inaccurate as the timer might have been stopped even when the oscillations were not finished yet. Thus, this would lead to an increase in chances of having inaccuracy in our readings.

However this weakness is considered minor since we are doing 10+ oscillations, thus we are dealing with it. To get rid of this weakness, we could do practice trials to see whether or not the time values are very close to one another, hinting us that our reaction time is pretty good therefore giving us accurate readings and results and overall, an accurate spring constant. Also, another way we could prevent this error is by getting mean averages to insure better accuracy if our reaction times alter the results.

Weakness: Another weakness could have been that the masses we were using contained quite a lot of impurities which had mass that was added to the masses we were working with. This could have increased inaccuracy within our results. To improve this, we should simply just measure each weight every time. Another suggestion could be that we should most probably just rinse off the impurities by using distilled water. That will in the end supply us with the original mass we were initially planning to work with.

Weakness: A weakness of this experiment would be the fact that at the 700 g point, the spring kept deforming which might have surely led to some inaccurate results. This systematic error may surely have altered the uncertainty value as it could have either increased it or decreased it. This could have easily caused inaccuracy since the uncertainties wouldn’t be calculated correctly like they were supposed to. To get rid of this weakness, we could have worked with several springs with that same mass causing all the deformation. Until we got a value without the spring deforming, we should carry on attempting to get a value for that mass.

Up till a minimum amount of 5 attempts should be made with the springs to avoid deformation. If the deformation keeps continuing, then it is safe to say that the mass cannot be worked with. Also, another suggestion would simply be to just avoid high weights if they cannot be worked with. Weakness: The spring was starting to deform even before and during the mass of 700g was experimented with. The deformation wasn’t as much compared to when 800g were taken however we were still able to identify deformation taking place within the spring.

Improvements: To improve this weakness, we should use experiment with masses which are between the masses I worked with. For example, instead of taking 500g, 600g and 700g, we could just take 550g, 600g, 650g and so forth. Weakness: Another weakness would be that damping might have taken place during our experiment which might have affected the accuracy of our results. The type of damping which might have occurred in our experiment would be light damping because we were working with air. In light damping, if the opposing forces are small, the result is a gradual loss of total energy.

This means that the amplitude of the motion gets slowly less with time. For example, our mass on a spring hanging in the air would have a little damping due to air resistance. Improvements: The way to avoid this weakness might be to take even more trials and work with more oscillations as that will reduce chances of error and we would get more accurate values and uncertainties in the end. Light damping due to air resistance normally occurs. However to avoid it, we should try and be more accurate to keep errors due to damping at its minimal.

This we can do by working with more trials and oscillations. Also, we should include balancing with number of oscillations. Meaning that too many could result in more damping effects. Lastly a very minor weakness could be the atmosphere we were working with. This is because the AC could have supplied the spring with more movement and motion. This could have caused a decrease in time and an increase in the spring constant k. The way to avoid this weakness is to basically turn off the AC and work with a normal atmosphere.

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