A pendulum swings through an arc of 56 cm. If each subsequent swing is 92% of the preceding one, what is the total distance covered by the time it comes to a complete rest?

Question

math&ing001 · Answer

It's a sequence like U(n+1) = 0.92*U(n)

anonymous · Answer

@math&ing001 What formula is that?

math&ing001 · Answer

That's called a geometric series, and they're asking you to calculate it's sum. From the formula above you get U(n) = 56 *(0.92)^n

anonymous · Answer

@math&ing001 Isn't the formula U(n) = a(1st term) * r^(n-1) ?

math&ing001 · Answer

Yep ! Except it's r^n

math&ing001 · Answer

Its sum from 0 to N is:
S = 56 * (1-(0.92)^N) / (1-0.92)
When N -> infinity, (0.92)^N -> 0
So we get:

S= 56/0.08 = 700
The total distance covered by the time it comes to a complete rest will be 700cm

anonymous · Answer

@math&ing001 Really?  The answer written here is 1344 cm....

math&ing001 · Answer

Can you redo the calculations for me please. This is the formula : http://en.wikipedia.org/wiki/Geometric_series#Formula

anonymous · Answer

@math&ing001 I got the same answer as you... I guess the answer here is wrong then. Thanks!

math&ing001 · Answer

Welcome !