Pendulum Period

Description

by Dr. D.G. Simpson, http://www.pgccphy.net/1030/software.html

Given the length L and amplitude θ of a simple plane pendulum, this program finds the exact period T , using the arithmetic-geometric mean method.

To run the program, enter:
L ENTER θ f A

where L is in meters and θ is in degrees. The program returns the period T in seconds.
After running the program, the calculator will be set to degrees mode.

Example:
Let L = 1.2 m and θ = 65°. Enter the above program, then type:

1.2 ENTER 65 f A

The program returns T = 2.3898 sec.

Program Resources

Labels

Name Description
 A Main program
 0

Storage Registers

Name Description
.0 Stores the angle
.1 Stores the length
.2
.3
.4 Count variable

Program

Line Display Key Sequence Line Display Key Sequence Line Display Key Sequence
000 019 11 √x̅ 038 11 √x̅
001 42,21,11 f LBL A 020 44 .3 STO . 3 039 44 .3 STO . 3
002 43 7 g DEG 021 1 1 040 42, 6, .4 f ISG . 4
003 44 .0 STO . 0 022 48 . 041 22 0 GTO 0
004 34 x↔y 023 0 0 042 45 .1 RCL . 1
005 44 .1 STO . 1 024 1 1 043 9 9
006 1 1 025 44 .4 STO . 4 044 48 .
007 45 .0 RCL . 0 026 42,21, 0 f LBL 0 045 8 8
008 2 2 027 45 .2 RCL . 2 046 10 ÷
009 10 ÷ 028 36 ENTER 047 11 √x̅
010 24 COS 029 36 ENTER 048 2 2
011 40 + 030 45 .3 RCL . 3 049 20 ×
012 2 2 031 40 + 050 43 26 g π
013 10 ÷ 032 2 2 051 20 ×
014 44 .2 STO . 2 033 10 ÷ 052 45 .2 RCL . 2
015 45 .0 RCL . 0 034 44 .2 STO . 2 053 10 ÷
016 2 2 035 33 R⬇ 054 43 32 g RTN
017 10 ÷ 036 45 .3 RCL . 3
018 24 COS 037 20 ×