User Commands  - pendulum (1)

NAME
pendulum(1f) - [PHYSICS] calculate pendulum period (LICENSE:PD)

CONTENTS

Synopsis
Description
Options
Examples
Author
License

SYNOPSIS
pendulum [ -length Length_In_Feet ][ -verbose]|[ --help]|[ --version]

DESCRIPTION
Given the length to the center of gravity from the fulcrum (pivot point) of a pendulum in feet calculate the pendulum frequency in swings/sec, and how long the swing takes (the period of the pendulum).

If the pendulum weight or bob of a simple pendulum is pulled to a relatively small angle and let go, it will swing back and forth at a regular frequency. If damping effects from air resistance and friction are negligible, equations concerning the frequency and period of the the pendulum, as well as the length of the string can be calculated.

The period of the motion for a pendulum is how long it takes to swing back-and-forth, measured in seconds. The period equation is: 

      T = 2*PI*sqrt(L/g)
The frequency of a pendulum is how many back-and-forth swings there are in a second, measured in hertz. Frequency f is the reciprocal of the period T: 

      f = 1/T
Therefore in terms of the length the frequency is 

      f = [ sqrt(g/L)]/2
The length equations are: 

      L = g/(4*PI**2*f**2)
and 

      L = (g*T**2)/(4*PI**2)
The generally accepted length of a seconds pendulum at sea level, lat. 45 degrees, is 99.356 cm or 39.116 in. = 3.25966 feet.

OPTIONS
-length Length_In_Feet
  distance from pivot point to center of gravity of pendulum.
-verbose [T|F]
  verbose mode, default is .true. .
--help display this help and exit
--version
  output version information and exit

EXAMPLES
Sample command lines ... 

   # A 1/4 of a meter pendulum has a period of about 1 second.
   pendulum -length 0.820209980
   For a pendulum with length  0.820209980      feet
   The frequency of the pendulum is  0.996806502     swings/sec.
   Each swing takes   1.00320375     sec.


   pendulum -length 3.00
   For a pendulum with length   3.00000000      feet
   The frequency of the pendulum is  0.287753224     swings/sec.
   Each swing takes   3.47519994     sec.

AUTHOR
John S. Urban

LICENSE
Public Domain

Nemo Release 3.1 pendulum (1) February 23, 2025
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