# Pendulum

phgao
Posers and Puzzles 30 Jul '05 08:09
1. 30 Jul '05 08:09
The length of a pendulum is 20cm. If the tip of the pendulum swings through an angle of 86 degrees, find :

a) The arc length ABC (the distance through which the tip travels)
b) The area of triangle OAC.
c) The area of the sector.
d) The area of the minor segment.
e) The length BX.
2. 30 Jul '05 08:11
Where are A, B, C, O and X? I picture would be nice ðŸ™‚
3. 30 Jul '05 11:241 edit
Assuming O is the center of the movement (where the pendulum is attached), A and C are the extremes, B is in the middle, and O is the intersection of AC and OB, I get (approximately):
a) 30 cm
b) 200 cm² (199.5...)
c) 300 cm²
d) 100 cm² (100.5..)
e) 5.4 cm

miscalcs are very realistic though.
4. 30 Jul '05 15:41
5. 31 Jul '05 01:51
Originally posted by THUDandBLUNDER
T'n'B, you are wrong.

a) arc ABC = 20[86*(pi/180)]
b) (1/2)(20)(20)sin(86deg)
c) (1/2)(20)(30)
d) 300 -199.5
e) 20 -20cos(43deg)
6. 31 Jul '05 03:02
what's with your profile phgao ?
7. 31 Jul '05 03:221 edit
Originally posted by phgao
T'n'B, you are wrong.
Maybe, but it doesn't seem like a puzzle to me. Just straightforward school maths.
8. 31 Jul '05 03:30
i like math
9. 31 Jul '05 08:53
Originally posted by THUDandBLUNDER
Maybe, but it doesn't seem like a puzzle to me. Just straightforward school maths.
40 years after school, straightforward math looks like a puzzle ðŸ™‚
10. 31 Jul '05 15:51
Originally posted by Mephisto2
40 years after school, straightforward math looks like a puzzle ðŸ™‚

my rec.

If only I could remember how to get the square root of a number using only paper and pencil... :'(

11. 31 Jul '05 15:59
Originally posted by LittleBear

If only I could remember how to get the square root of a number using only paper and pencil... :'(
Check this ðŸ™‚
http://www.bbc.co.uk/dna/h2g2/A827453

12. sonhouse
Fast and Curious
01 Aug '05 17:47
Originally posted by ilywrin
Check this ðŸ™‚
http://www.bbc.co.uk/dna/h2g2/A827453

wow, that brings back memories, learned that one when I was in
grade school at the First Lutheran School in El Monte California.
Wonder how you would do it for cube roots? can this method be
generalized for Nth roots?
13. 01 Aug '05 18:27
Originally posted by sonhouse
wow, that brings back memories, learned that one when I was in
grade school at the First Lutheran School in El Monte California.
Wonder how you would do it for cube roots? can this method be
generalized for Nth roots?
Well i just did a little googling and found this generalization ðŸ™‚
http://en.wikipedia.org/wiki/Shifting_nth-root_algorithm

14. sonhouse
Fast and Curious
02 Aug '05 02:14
Originally posted by ilywrin
Well i just did a little googling and found this generalization ðŸ™‚
http://en.wikipedia.org/wiki/Shifting_nth-root_algorithm

wow, lets hope we don't lose our calculators!ðŸ™‚
15. 02 Aug '05 03:03
Originally posted by LittleBear

my rec.

If only I could remember how to get the square root of a number using only paper and pencil... :'(

For square root, I recommend using the "Divide and Average" algorithm. It has quadratic convergence (ie, it smokes), and it can be generalized for nth root. From what I see in the algorithms presented here, they seem to have linear convergence (ie, they're slow).

Here's Divide and Average.

Say you want to find the square root of the number k.

Set X(0) to be a guess of the square root of k.

Now, set X(n+1) = (1/2)*(X(n)+(k/(X(n))).

Another good thing about Divide and Average is that if you make a mistake, your mistake gets smaller, and smaller with every iteration. With linear convergence methods, if you make a mistake, your results are worthless, regardless of how far you carry the calculation after your mistake. With Divide and Average, you can make a mistake at every step, and each mistake gets damped more and more, as you iterate, so you always approach the answer you are interested in.