Pendulum Problem?

Question

A pendulum is released to swing freely. On the first swing, the pendulum travels a distance of 18 inches. On each successive swing, the pendulum travels 90%of the distance of the previous swing. What is the total distance the pendulum swings? After how many swings has the pendulum traveled 80% of its total distance?

FYI i already have the answer, it's in the back of the book. I just don't know how to derive at the answer.

Answer 1

The swing distance follows an exponential decay.

1st swing-> x
2nd swing-> 0.9 x
3rd swing-> 0.9*0.9 x
4th swing-> 0.9*0.9*0.9 x

and so on

This is a geometric series.

http://en.wikipedia.org/wiki/Geometric_progression

The solution for a geometric series is

Sum[y^n,{n,0,infinity}]=
1/(1-y)
(for y<1)
From this information you should be able to solve the problem completely.

Answer 2

do you're own dang homework, CHEATER!