Posted in Physics Revision

Pendulums

P3 3.6

Definition: a bob (a mass) swinging on a string.

For example, a playground swing, with the mass being the person on the seat.

How it works: The swing of a pendulum can be described by its:

  • amplitude → how far from the vertical (the dotted line on the diagram) the string moves.
  • time period → time taken for one complete swing.
  • frequency → number of complete swings per second.

When a pendulum is swinging we say it is oscillating.

Image result for swinging pendulum
Source

The time period is directly proportional to the square root of the length of the string:t vs length

The frequency of the oscillations is equal to 1 divided by the time period:

f = 1 over t

T = time period → unit: seconds (s)

f = frequency → unit: Hertz (Hz)

L = length → unit: metres (m)   examiners often trip students up by using cm or mm. Ensure you have converted all units before beginning your calculations.

We can conclude by looking at the equations that:

the longer the pendulum → the longer the time period → the smaller the frequency

The time period of a pendulum can be affected by:

  • mass of the bob
  • length of the string
  • amplitude

Random Errors

Definition: an unpredictable variation around the true value, causing each reading to be slightly different.

So, basically, mistakes. These are often human errors. One very common, and unavoidable, human error is the reaction time error.

As you know, it takes us a moment to react, for example, there will be some time between releasing the pendulum to swing and starting the stopwatch.

This is on average 0.2 seconds in humans.

To reduce the impact of this reaction time on results, record the time it takes for several oscillations to occur, such as 10 or 15, and then find the average. This will make reaction time almost negligible.

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