Investigate the factors which affect the period of one swing (oscillation) of a simple pendulum.

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Pendulum

Aim: To investigate the factors which affect the period of one swing (oscillation) of a simple pendulum. The factors I will use are length of the string, and angle that the bob is released from.

Hypothesis:

1. Length of string

I think that the length of the string directly affects the period of one oscillation.  The mathematical formula used to describe the period of the pendulum is:

T= 2 π/g

T is the period (time for one swing - seconds)

 is the length of the pendulum (metres)

g is the acceleration dues to gravity. (N/KG)

 (Length) is in the formula, clearly indicating that it is a factor which will directly affect the period of time.

To see whether the time period will increase or decrease when the length is increased, I will substitute the formula for numbers to see the result.

Length 0.3, g-force = 9.8N/KG

T= 2π √/g

T = 2π √0.3/9.8

T = 1.009s

Length 0.4, g-force = 9.8N/KG

T= 2π √/g

T = 2π √0.4/9.8

T = 1.269s

The calculations above show that when the length of the pendulum is 0.3m, the time for one oscillation is 1.009s.  When the length is increased, the time is increased.  When length is 0.4m, time period is 1.269s.

This tells us that when the length is increased, the time period is increased.

2. Angle of release

A simple pendulum is only a weight known as a “bob” hung from a string.  When the bob is lifted, the pendulum gains potential gravitational energy, as it is acting against the force.  Therefore, the angle, which would raise the height, would give the bob more gravitational energy (up to 90°).  The more the angle, the more the energy, the faster the swing, the less the period of time.

Prediction:

1. Length of string – I predict that the longer the length of string, the longer the period of one oscillation.

2. Angle of release – I predict that the more the angle the less the period of time, but this only applies up to 90°

Apparatus:

  • Clamp stand
  • String
  • Bob
  • String
  • Protractor
  • Ruler
  • Stopwatch

Method

  • Set up the clamp stand, quite high on a stand and place at the edge of the table.  Tie a string with a bob at the end (a simple pendulum) onto the clamp.
  • Allow the pendulum to swing freely, and ensure that the stand is steady on the table.  If it is shaking, the weight may allow the pendulum to move faster, or slow it down, and this could affect our results.
  • Attach a protractor to the clamp so that the angle of release can easily be measured.  This is needed for all experiments because the angle has to be constant in the other experiments.
  • Swing the pendulum from a particular angle of release, and make sure that the same angle is used for the whole experiment.
  • Start the stopwatch when the bob is released, in order to measure the time period of 10 oscillations.  10 is a good number to choose, because it is not too small, or the results may not be accurate.
  •   Repeat the experiment again, changing the independent variable every time.  In the case of length, I did the ranges
    5-50, going up in 5s, and in the angle of release I did 10-90°, going up in 10s.
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Variables

1. Length of string 

Independent: Length of string

Dependant: time period of 10 oscillations

Control:

  • Angle of release
  • Height from ground
  • Position of pendulum
  • Mass of bob

2. Angle of release 

Independent: Angle of release

Dependant: Time period of 10 oscillations

Control:

  • Length of string
  • Height from ground
  • Position of pendulum
  • Mass of bob

Conclusion

A pendulum is something hanging from a fixed point which, when pulled back and released, is free to swing down by gravity and then out ...

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Here's what a star student thought of this essay

The student's grammar and spelling is fine and so is his layout. However he should of made repeats and calculated an average to increase reliability, and he should of made a table for each of his experiments. He could of also plotted a graph to determine how his variables are proportional to each other.

The student clearly lays out his method which I would recommend always doing as it is best to know what you are doing before you do it, you don't want to be confused as to what to do when you get to the experiment. He calculates all his errors which is very helpful as it both adds depth to the coursework and helps to stop you from making incorrect conclusions, as you can see if the results could be due to errors. However he works out the error by comparing it to how the theory predicts the result should be, you should not do this. Make sure to calculate errors the regular way. He uses theory to calculate why the speed is not determined by the mass of the bob, which adds a lot of depth. However it could have been done easier by realise that the force is determined by the mass, but so is the acceleration, therefore since F=ma, since F is the mass multiplied by another value, you can put the equation as mk=ma, and the mas cancel. You could go into more depth and determine what determines k.

This is a good essay that ties experiment and theory together quite well. The student has answered the question of what factors affect the time period of an oscillation well. He has at first looked at his theory to determine that length will likely determine the time period, and he has also used his initiative to think that angle and mass may affect the time period even though the theory says they do not. He has made a prediction based on his theory and on his intuition, however I would of recommended rather than just going on intuition he should of checked his theory to see what the theory predicts would happen in terms of increase in mass and increase in angle.