RESULTS:
Length = 32+0.2cm, amplitude = 6 +0.2cm
Weight vs Time of a pendulum
Length = 32 + 0.2cm, mass = 99.89g + 0.01g
Amplitude of Swing vs Time of a Pendulum
Amplitude = 6+0.2cm, mass = 99.89 + 0.01g
Length of String vs Time of a Pendulum
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
Gemma: 34cm - timed –
t = √(2x/g) = 0.26 sec
Caitlin: 63cm - released the bob - 0.36 sec
Since Gemma stopped and started the stopwatch, her reaction time roughly cancels each other out. However, Caitlin’s reaction time (0.36 sec) must be taken into account. But since Caitlin released the bob simultaneous to Gemma’s starting of the stopwatch, Gemma’s reaction time must be taken away from Caitlin’s to see the uncertainty (0.36-0.26 = 0.1s) This was not taken into account when drawing the uncertainties on the graph.
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.
DISSCUSSION & EVALUATION:
Factors that also affect the period of a pendulum that are not investigated in this practical are the wind, the latitude of the pendulum, the force of push by the individual, the type of bob or string, whether the bob is swing in a straight line or in a circular shape and whether the bob bounced or not. The main sources of error include reaction time, the uncertainty of the measurement made by the ruler and the stopwatch and the limit of reading. The result could be improved by letting only one individual let go and start the stopwatch - the reaction time being the same should provide more accurate results. Another thing that could be improved is to not start the stopwatch on the first swing. Instead, wait till the bob reaches its starting point again before starting the stopwatch. This will make the results more reliable as in the first swing; the amplitude will be greater than the amplitude for the period of a pendulum. However, this may have no affect as factors such as wind resistance and friction will slowly decrease the period of a pendulum and eventually the pendulum will stop. This is another factor not taken into account. This experiment was conducted under the assumption that the motion is monotonous – that is, that each period of the pendulum is the same. To minimise the effect friction and wind resistance may have, the experiment could be improved by being conducted in an environment that will not affect the period of a pendulum as much. The friction cannot be helped. Also, the graph of Length Vs Time of a Pendulum shows that the line does not go through the origin and the reason given was that the line may be a curved line. To prove this, the next experiment conducted could test a wider range of points. Another factor that affects the period of a pendulum is whether the bob bounced or not and whether it swung in a straight line or in a circular motion. The only thing that can be recommended for this source of error is added caution.
CONCLUSION:
Drawing conclusions from this practical, one can assume that the mass of a bob does not affect the period of a pendulum. 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: