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# Simple Harmonic Motion Essay

Abstract

Through examining the simple harmonic motion of a mass hanging on a spring, three investigations were conducted in the experiment. The experiments include the relation between the period in oscillations and mass, and figuring out if the period vs. mass graph should go through the origin and lastly, finding the mass needed to create a one second timer. It was investigated by placing a motion detector under a spring that was attached to a clamp which was attached to a retort stand. The mass was pushed above its equilibrium and the position vs. time graph was recorded. It was found that it was related by P(s) = 0.04m^0.5, it would take 625 g to make it a 1s timer and the graph would pass through the origin.

Purpose:

When a mass hanging on a spring is raised above the equilibrium position and released, it goes through simple harmonic motion. This experiment was performed to find the relation between period and mass and to find how much mass would be needed to use this as a 1s timer The Method

Equipment

The equipment that were used in the experiment are a motion detector, 30 cm rule, a set of mass, computer(LoggerPro), spring, retort stand and clamps.

Procedure

1. A clamp was attached to a retort stand and a spring was hanging from the clamp. The motion detector was placed right underneath the spring. A mass (50g, 70g, 200g, 250g, 400g, and 500g) was attached to the end of the spring. It was made sure the mass was at least 20 cm above the motion detector. 2. The mass was raised above the equilibrium to start the simple harmonic motion, and then the motion detector generated a position vs. time graph on loggerpro. 3. Then the mass was changed and the steps were recorded until there were 6 positions vs. time graphs of 6 different masses.

A Plot of Period vs. Mass from the data in table 1 is drawn in Graph 1. The graph shows that the Period of oscillation is proportional to the m^0.5. Also the graph shows the curve fit is P(s) = 0.04m^0.5, where P(s) represents the period in seconds and m represents mass.

Conclusion

As shown in Graph 1 that the period of oscillation [P(s)] is directly proportional to the mass^0.5 (m) on the spring it is related by the equation P(s) =0.04m^0.5 but the uncertainty is about 2% or less in mass and 1% or less in period so the uncertainty in the constant about 2-3% Also it should pass through (0, 0) graph. Having 0 as the x means there is no mass, and without mass, the spring would return to equilibrium but there will not be enough force of gravity to drag the spring below the equilibrium. It would take 625 g to make the spring a 1 second timer. In conclusion the period of oscillation is directly proportional to m^0.5, additionally the graph of period vs. mass has to pass through (0, 0).

Essay Topics:

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