Re: How can the decay of a simple pendulum be modeled mathematically?

Dear Luke

Every time your pendulum goes forward and backward it will loose some 
percentage of its "amplitude" (or max. angle or height), say 1%. Then, the 
amplitude a after n oszillations is a(n)=a0 0.99^n (the "^" means 0.99 to a 
power of n, a0 is the initial amplitude). Your problem consists of two 
parts: Test if the formula really describes the experiment and - if it 
does - find a number d (the damping which was 0.99 in my example). I 
recommend to plot your measurements in a special way. Take the logarithm 
log(a) of the ampitude on the y- axis and take n on the x-axis. The points 
should form a straight line if the formula is right ! The slope of this 
line taken to a power of 10 should give d (d=10^slope). 
(Why does that work ? Take the logarithm of the formula and use the rules 
log(a b)=log(a) + log (b) and log(a^b)=b log(a) and you'll get log(a)=a0+n 
log(d) )
If you find this too complicated you could also find d by playing with your 
calculator (trial and error method). Assume a number d (e.g. 0.98) and 
calculate the amplitude after say 20 oszillations using the formula. If the 
result is too small compared with experiment, then try something bigger 
e.g. 0.99.