
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. 