# B Large Amplitude Pendulum Equation

Tags:
1. Sep 17, 2016

### StevenJacobs990

The equation for large-angle pendulum can be infinitely long. What is the pattern with the latter numbers in "..."?

2. Sep 17, 2016

### sophiecentaur

Sorry, your attachment won't open for me.

3. Sep 17, 2016

### sophiecentaur

4. Sep 18, 2016

### StevenJacobs990

Yeah, but whats the pattern that comes after 11/3072 (theta)^4?

5. Sep 18, 2016

Staff Emeritus
There is no pattern. That's why you need the elliptic integrals.

6. Sep 18, 2016

### sophiecentaur

7. Sep 19, 2016

### StevenJacobs990

This is the attachment

8. Oct 10, 2016

### wolf1728

Here is a graphic I made.
Look at equation 3.

9. Oct 18, 2016

### wolf1728

StevenJacobs990
I don't know the equation for generating those numbers in the formula but here is the large amplitude formula carried out to theta 20:

10. Oct 18, 2016

### rumborak

Honestly, I wouldn't be surprised if this a Taylor expansion of some sort.

11. Oct 19, 2016

### sophiecentaur

. . . .or something else. There are (my Mathematician friends tell me) many equations that can only be solved using a series - Taylor or not so well known ones.

12. Oct 20, 2016

### wolf1728

I originally was writing a pendulum calculator and while researching the Internet, I came across this topic. Anyway, I finished the calculator and it is online: http://www.1728.org/pendulum.htm
It can calculate pendulum periods up to theta 14 and uses the arithmetic mean to calculate exact pendulum periods.
Try it out if you like.