Parameter B

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The period of the function was 1 second when B was equal to 6.28 (or 2\pi) because frequency is revolutions/second, and if the frequency is 2\pi/second, then we are going once around the unit circle every second. Once given the equation \omega=\sqrt{\frac{k}{m}}, it can quickly be reasoned that to double the frequency, the mass must be divided by 4 (2\omega=2\sqrt{\frac{k}{m}}\:\:\:\:\:,\:\:\:\:2\omega=\sqrt{4}\cdot\sqrt{\frac{k}{m}}\:\:\:\:,\:\:\:\:2\omega=\sqrt{\frac{4k}{m}}\:\:\:\:or\:\:\:\:2\omega=\sqrt{\frac{k}{\frac{1}{4}m}}). Our group decided to go one step beyond simply examining the relationship in theory. We tested 7 different masses against their B values, and developed this graph.

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Simple Harmonic Lab.JPG
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From this graph, we can determine easily that yes, our prediction of having to cut the mass by four would yield an angular frequency of two times what it was. Obviously from the given equation, the only other factor that plays a part in B is the k value of the spring being used.

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