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# Experiment to investigate the factors affecting the swing of a pendulum.

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Introduction

Title: Experiment to investigate the factors affecting the swing of a pendulum. Aim: To investigate how the period of oscillation of a pendulum is affected by the length of the string and the mass of the weight attached to the string. Introduction: A simple pendulum consists of a weight hanging at the end of a string. When a force is applied to the pendulum so that it is displaced by a small angle, the pendulum will swing to and fro at a constant rate under the effect of gravity. The path travelled by the weight is the arc of the pendulum and the period of the oscillation is the time taken for the weight to pass to and fro once over this arc. In this experiment I will be investigating how the period of oscillation of the pendulum is affected by: 1. The mass of the weight attached to the string 2. The length of the string. In this experiment, I will also determine the value of the acceleration due to gravity using the relationship between T; the period of the oscillation and L; the length of the string. Hypothesis: 1. I predict that the period of oscillation will increase with increasing length of string. This is because a longer string will travel a grater distance than a shorter string given the same angle of displacement. ...read more.

Middle

The time taken for 10 oscillations was measured using the stopwatch and recorded. The procedure was repeated using masses 100g, 150g, 200g, 250g and 300g. Two time readings were measured and recorded using each mass. The length of the string was kept constant at 40cm during the experiment. Results: Experiment 1: Length, L/cm Time, t1/s Time, t2/s 10 20 30 40 50 60 8.28 10.43 11.97 13.75 15.00 16.31 8.12 10.34 11.97 13.88 14.94 16.31 Experiment 2: Mass, m/g Time, t1/s Time, t2/s 50 100 150 200 250 300 13.76 13.88 13.88 13.78 14.00 13.84 13.80 13.78 13.84 13.82 13.78 13.94 Analysis of results: Experiment 1: Length, L/cm Time, t1/s Time, t2/s Time, t/s Period, T(t/10)/s 10 20 30 40 50 60 8.28 10.43 11.97 13.75 15.00 16.31 8.12 10.34 11.97 13.88 14.94 16.31 8.20 10.39 11.97 13.82 14.97 16.31 0.82 1.04 1.20 1.38 1.50 1.63 In the above table, time t/s was calculated by finding the average of the two time readings. The graph of length, L/cm against period, T/s was plotted and the following was noticed: 1. The graph does not start at the origin 2. There is a direct relationship between length of string and the period of oscillation. This thus shows that the period of oscillation increases with an increase in the length of the string. ...read more.

Conclusion

If the experiment were to be repeated, it will be better to measure the time for 50 oscillations instead of 10 used in my experiment. This is to ensure that the error that arises through being unable to start or stop the stopwatch when the pendulum is exactly in the intended position is greatly reduced. I expected the graphs of the period of oscillation against length and that of the square of the period of oscillation against length to start at the origin, but they did not. This may be due to experimental errors, for example, in measuring the time of oscillation or in the calibration of the metre rule used in measuring the length of the string used. The error was recurrent and therefore, a systematic error because although the graphs did not start at the origin, the graphs still show a direct proportionality between the period of oscillation and the length of the string. The value of the acceleration due to gravity calculated was 9.87ms-1 as opposed to 9.81ms-1, which is the well-known constant, used in physics today. The value I calculated was not quite right and this may be due to the experimental errors that have been carried over. If this experiment was to be carried out again and all the errors are taken into account and prevented, I think the experimental results will be more reliable. The effect of the angle through which the pendulum is displaced may also be investigated in further experiments. ...read more.

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