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PRACTICAL INVESTIGATION: THE SIMPLE PENDULUM AIM: The aim is to investigate the factors which affect the period of oscillation of a simple pendulum. THEORY: Over 400 years ago, Galileo came up with the theory that the period of a pendulum depends only on the length of the pendulum. A simple pendulum consists of a weight hanging off a string. When the bob is stationary, the two forces acting upon the bob - the tension of the string and gravity - equalise and gives the bob an overall force of 0N. However, when the bob is in motion, the forces are unbalanced and the bob swings back and forth. If the amplitude of the string is increased, the weight will swing back and forth at a regular period. However, if the amplitude of the swing is increased too much, this may cause the weight to bounce and the period of a pendulum may be void. The period of a pendulum is the time for one complete swing. The equation for the period of a pendulum is T = where 'L' is the length of the pendulum, 'g' is the acceleration due to gravity and 'T' is the period of a pendulum. However, when doing a practical, the period of a pendulum can be determined by measuring the time a pendulum takes to swing twenty periods and dividing the results by twenty.
Full Length (cm) + 0.2cm Trial 1 Trial 2 Trial 3 Average Period of motion (s) 15 15.37 15.46 15.78 15.54 + 0.24s 0.78 + 0.24s 20 18.06 18.18 18.22 18.15 + 0.09s 0.91 + 0.09s 26.5 20.22 20.66 20.78 20.56 + 0.34s 1.03 + 0.34s 33 22.97 23.00 22.98 22.98 + 0.02s 1.15 + 0.02s CALCULATIONS: Uncertainty: Limit of Reading: Lengths measured by ruler (amplitude/length of pendulum) - Smallest unit = 0.1cm There is uncertainty in the start and end of ruler (2 x 0.1cm = 0.2cm) Weights weighed (mass) - Smallest unit = 0.01g Average time and period of pendulum uncertainty: Greatest discrepancy - eg. Length (cm) - 33cm Trial 1 - 22.97s, Trial 2 - 23.00s, Trial 3 - 22.98s, Average - 22.98 Discrepancy - Trial 1 - 0.01s, Trial 2 - 0.02s, Trial 3 - 0.00s Uncertainty: 0.02s ANALYSIS OF RESULTS: The graph of Length Vs Time of a Pendulum shows a clear relationship between the length of a pendulum and the period of a pendulum. In the graph of Length Vs Time of a Pendulum, the line of best fit does not go through the origin. This could be due to the fact that the line may not be a straight line but a curved line that will go through the origin. The graph of L-2 Vs Time of a Pendulum shows a clear linear and proportional relationship between the two variables.
This may be due to the fact that although more mass would slow the pendulum down when the bob is ascending, this added mass will also give the pendulum more momentum and therefore make the pendulum descend more quickly. Again, drawing conclusions from this experiment, it can be seen that the amplitude of the swing does not affect the period of a pendulum. Although there are varying results, no definite conclusion can be draw from the data. This experiment also shows the length of a pendulum does affect the period of a pendulum. Also, it shows that the relationship between the square root of the length and the period of a pendulum is linear and proportional. This conclusion is very accurate as all the points lie on the line of best fit. The proves that Galileo's theory was partly correct when he predicted that only the period of a pendulum was only dependent on the length of the pendulum and not on the mass of the pendulum or the amplitude of the swing. This also proves the hypothesis was partially correct when it states that the factor that will greatly affect the period of the pendulum was the length of the pendulum. The part that both theories failed to recognise was that the period of a pendulum was dependent on the square root of length and not the length. This experiment investigated the factors which affect the period of oscillation of a simple pendulum. Sources: http://www.8886.co.uk/pendex1.htm http://cc.ysu.edu/physics-astro/Report.PDF
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