Question

A pendulum bob swings 4.0 cm on its first oscillation. On each subsequent oscillation the bob travels 3/4 the previous distance. Find the total distance the bob travels before coming to a rest.

Answer 1

geometric series... A_n = 4*(3/4)^(n-1)
find infinite sum of series
--> S_n = 4/(1-3/4)

Answer 2

\[a+ar+ar^2+ar^3+...=\frac{a}{1-r}\] so long as \(-1<r<1\) in your case \(a=4,r=\frac{3}{4}\)

Answer 3

so -.5 or -1/2?

Answer 4

neither
the problem asks "what is the total distance" so the answer must be positive
did you calculate \(\frac{4}{1-\frac{3}{4}}\) ?

Answer 5

oh, sorry i was going off the first guys equation. so its -.16?

Answer 6

hold on lets go slow

Answer 7

16, not .16 sorry

Answer 8

the answer is clearly a positive number right? it is asking for a distance
"Find the total distance ..."

Answer 9

ah yes, it is 16

Answer 10

great thanks

Answer 11

yw