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investigation of a simple pendulum

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Siddharth Nair

         10 C


Aim: To verify the dependence of the Time Period of a Simple Pendulum on its Length. This should be done according to the direct proportionality of T^2 on L, by drawing a graph between them and obtaining a straight line.


A pendulum consists of a mass also known as a bob, attached by a string to a pivot point. As the pendulum moves it ‘draws’ out a circular arc, moving back and forth in a periodic fashion. Neglecting air resistance, there are only two forces acting upon the pendulum bob. One of these forces is gravity. The force of gravity acts in a downward direction and does work upon the pendulum bob. However, gravity is an internal force and therefore does not serve to change the total amount of mechanical energy of the bob. The other force acting upon the bob is the force of tension. Tension is an external force, and if it did do work upon the pendulum bob it would serve to change the total mechanical energy of the bob. The force of tension does not do work since it always acts in a direction perpendicular to the motion of the bob. At all points in the trajectory of the pendulum bob, the angle between the force of tension and its instantaneous displacement is 90 degrees.

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-35 cm

-40 cm

-45 cm

-50 cm

  1. Record all your readings, and display them in a tabular format.

Data collection table

Length of string (cm)

Time taken for 10 oscillations (s)

Reading 1Reading 2

























  • Processed Data collection table:

Formulas used:

Average of 2 readings=  reading 1+ reading 2


Time taken for 1 oscillation=   Time taken (T)

                                             Number of oscillations (10)

Final time used for graph= time taken for one oscillation^2 (T^2)

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th oscillation might not have been the same.The hold on the thread could have differed (the thread might have been put differently into the cork, making the hold different)Wind in the room could have affected the time taken to complete 10 oscillations.Even though the stand was held in place to avoid it shaking, lack of concentration, or a slack grip could have resulted in the stand shaking.

While doing the experiment, we saw other people swinging their pendulum from a certain angle, with the use of the protractor, for all their tests. As we knew that the angle would not make a difference to the time period, so we had not used a protractor for our tests, we verified our knowledge, by doing a few tests, and these were the results:

(The length of the string was kept as 20cm)

Angle of Pendulum (From Stand)

Time taken for 10 oscillations (s)

Oscillation Period (s)










Each oscillation took 0.9seconds. The millisecond has not been included, as that could be different due to human reaction time not being the same in all cases. These results merely show that you do not need to swing the pendulum from the same angle, as a constant, in order to derive accurate results. Therefore, not using the same angle for all the tests could not have been an error, on our part.

Note:  implementing the points shown to make it a ‘fair’ test reduced the margin of error.

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3 star(s)

Response to the question

The student has answered the question of how the time period of a pendulum is dependent on length very well. They have started off with their hypothesis and explaining why they believe this to be what will occur, using their ...

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Response to the question

The student has answered the question of how the time period of a pendulum is dependent on length very well. They have started off with their hypothesis and explaining why they believe this to be what will occur, using their theory to back it up. I would always recommend backing up whatever you claim with theory, as this is generally where the marks come from. He has made a table and graph that back up his prediction very well.

Level of analysis

He has managed to manipulate his equation to plot a graph that will result as a straight line, showing that T^2 is proportional to l. Always make sure to see if you can manipulate your equations to work out how the values are proportional. He should of however made more repeats than just 2. He works out the errors in his equipment but not the errors in his overall measurements, which I would recommend as the errors in his overall measurements in this case, are much higher.

Quality of writing

I would recommend using SI units, meters instead of cm, but in this case it is not very important. Just be careful if you don't use SI units, as you could go wrong with some equations if you do not use SI units. He also should have plotted a line of best fit rather than joining dot to dot, you will always lose marks if you plot dot to dot. He could have then used his gradient to calculate g using his equation to figure out how. This would help add some more depth to his coursework.

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Reviewed by jackhli 28/02/2012

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