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Mechanics
 
Aim: to show that the amplitude of the motion of a pendulum, oscillating in air, decreases exponentially with time/number of oscillations
See Mechanical Oscillations, Exponential Graphs
 
 
Method
The measurements will be rather approximate but, if you are careful, you should be able to show that the amplitude of the damped oscillations decreases exponentially.
To be sure that the damping is easily measurable, use a relatively small mass (5g or 10g on a pendulum of around 30cm length should be ok).
 
Try to estimate the amplitude after 10, 20 etc oscillations.
Two experimental arrangements are shown below
1. place a ruler approximately as shown in the diagram on the left below or
2. mark out an angular scale on a sheet of paper placed near the pendulum.
NB the second alternative is probably more convenient if you have a pendulum made from a thin strip of metal or similar. If the pendulum is made using a thread, the bob will tend to develop an elliptical (rather than rectilinear) motion... if fact, now I come to think of it, this is true of both methods... get yourself a rigid pendulum if possible!
Allow the pendulum to oscillate and estimate the amplitude of the oscillations after 10, 20, 30 etc oscillations.
Plot a graph of amplitude against number of oscillations.
Try to prove that this graph is (approximately) exponential.
 
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