Graph Plot a graph of distance (l ), measured in metres, against time squared (T2 ), measured in seconds squared, with time squared on the y-axis.
Conclusion
The straight line through the origin shows that distance is proportional to time squared. Use Graph
Acceleration due to gravity can be calculated from the graph. If the time squared is on the y-axis and length on the
x-axis, then acceleration due to gravity is 42 divided by the slope of the line of best fit Explanation
Based on the equation for periodic time of a simple pendulum we get: T 2pAgQT2 4p2
l g l
Using the equation of the line y mx c, given that c 0 because the line passes through the origin, it is clear that acceleration due to gravity is 42 divided by the slope.
Precautions Ensure the maximum angle opened up by the pendulum is less than 5 from vertical. The angle must be less than 5° to allow us to assume (i) the motion is SHM and (ii) the force causing the acceleration is directly proportional to g.
Ensure that the pendulum oscillates in one plane only. Make sure there are no draughts in the room. Use a small heavy bob to reduce air resistance and to ensure the string remains taut and at full length. Do not allow the bob to spin. Use an inextensible string so that the length of the pendulum remains constant. Clamp the string between two coins or a split cork so that the length of the pendulum remains constant. Use large values for l; this will reduce the percentage error. Allow for a greater number of oscillations; this will reduce the percentage error on the periodic time. Use a more accurate timer; light gates, data logger and calculator could be used.
Note
The experiment can be repeated with bobs of different masses to show that the periodic time of the pendulum is independent of the mass of the bob.
‘SECTION A’ EXPERIMENTQUESTIONS
Q1 In order to investigate the relationship between the period and the length of a simple pendulum, a pendulum was set up so that it could swing freely about a fixed point.The length l of the pendulum and the time t taken for 40 oscillations of swing through a small angle were recorded.The length of the pendulum was increased and the procedure was repeated.
