## Harmonic Motion lab

We have conducted an experiment to verify the Law of Conservation of Energy as presented in Simple Harmonic Motion. The Law of Conservation of Energy is one of the most vital laws in physics. It serves as a basis for many theoretical calculations and inventions, which is precisely the reason why we decided on conducting a verification experiment on this law. This could be done using several methods, but as creating a system with fully elastic collisions is prone to have a high degree of inaccuracy, we decided on creating a mass-spring system on an air track.

We tried to achieve the verification of the Law of Conservation of Energy using the mass-spring system through two steps: we measured the spring constant (k) of a dynamometer, using weights, rulers with accordance to the equation for the weight of the object and Hooke’s law: Equation for weight: F=mg , where F – force working on the object (due to gravity), m – mass of weight, g – gravitational acceleration.

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Hooke’s law: , where k – spring constant, x – extension of spring, F – force working on the spring (note that it is due to the object attached – here our weight). What is worth mentioning is that a dynamometer is essentially a spring adjusted to show the respective force on given extension, which means that using weights and calculating the force due to gravity was not necessary, but it was a valuable exercise and allowed us to verify the accuracy of the mentioned adjustment of the dynamometer.

When using springs that are not dynamometers, however, one should use weights (or a similar method) to find the spring constant. After this part of the experiment was over, we verified the found k of the dynamometer using an air track – we would extend the spring of the same dynamometer by a set length (amplitude of the simple harmonic motion – x0) and release it, after which we would measure the gained velocity (velocity at equilibrium – vmax) of the returning block (of mass m) using photoreceptors.

As the system is on an air track and as such is considered to not be under the effects of friction, velocity measured is assumed to be the maximum velocity gained by the block in equilibrium. It is worth noting that we did not measure velocity directly. Using photoreceptors we solely measured the time (t) it takes for the block to move through a set distance (s). Having this data we calculated vmax with the well-known equation:

As for setting of the mass-spring system, we used two different masses of the blocks and five different extensions per each mass, as to acquire accurate results, which are very important especially for verification experiments. For calculating k found using the air-track we used the equation for the Law of Conservation of Energy in simple harmonic motion. As the air-track is horizontal (gravitational potential energy is considered to be constant), we assume that only elastic potential energy and kinetic energy are interchanged.

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