Equation for the Period of a Pendulum

  • Thread starter Thread starter Spoon.
  • Start date Start date
  • Tags Tags
    Pendulum Period
Click For Summary
SUMMARY

The period of a pendulum is defined by the equation T = 2π√(l/g), where T is the period, l is the length of the pendulum, and g is the acceleration due to gravity. The discussion highlights the derivation of this equation and the significance of plotting Log T vs Log L, where the slope of approximately 0.404 indicates a relationship between the logarithm of the period and the logarithm of the length. This slope suggests a power-law relationship, which can be further analyzed by taking the logarithm of both sides of the original equation.

PREREQUISITES
  • Understanding of basic physics concepts, particularly pendulum motion
  • Familiarity with logarithmic functions and their properties
  • Knowledge of graphing techniques and slope interpretation
  • Basic mathematical skills for manipulating equations
NEXT STEPS
  • Study the derivation of the pendulum period equation in detail
  • Learn about power-law relationships in physics
  • Explore the implications of logarithmic transformations in data analysis
  • Investigate the effects of varying gravitational acceleration on pendulum motion
USEFUL FOR

Students of physics, educators teaching mechanics, and anyone interested in the mathematical modeling of oscillatory motion.

Spoon.
Messages
5
Reaction score
0
Hey, I know that the equation to find the period of a pendulum is

T = 2\pi\sqrt{\frac{l}{g}}

and my question is how exactly did they derive this? I've done some research and it confused me even more, can someone please explain the procedure to derive this equation?

Thanks.
 
Last edited:
Physics news on Phys.org
Ok I got that figured out. Thanks so much!

But I have another question...

I am to plot Log T vs Log L, where L is length of the pendulum and T is the period. I graphed this and found the slope to be around 0.404. What is significant about this slope and how does it show the relationship between L and T?

I think I'm suppose to find the equation of the line?

Thanks.
 
Last edited:
Take the log of both sides of the Simple Pendulum equation, what is the slope of the line?
 

Similar threads

JEE solution wrong? (tempco of a clock)
  • · Replies 14 ·
Replies
14
Views
2K
Looking for observed rotation periods of various Foucault pendulums at different latitudes
  • · Replies 6 ·
Replies
6
Views
1K
The period of a simple pendulum
  • · Replies 20 ·
Replies
20
Views
2K
Period of a Pendulum on the Moon
  • · Replies 7 ·
Replies
7
Views
4K
Derivation of time period for physical pendula without calculus
  • · Replies 3 ·
Replies
3
Views
2K
Foucault Pendulum at the North Pole
  • · Replies 9 ·
Replies
9
Views
2K
Period of simple pendulum on an inclined moving platform
  • · Replies 20 ·
Replies
20
Views
3K
Seeking advice on "simple" pendulum problem
  • · Replies 27 ·
Replies
27
Views
2K
Differential Equation of a Pendulum
  • · Replies 32 ·
2
Replies
32
Views
2K
Coupled oscillators -- period of normal modes
  • · Replies 11 ·
Replies
11
Views
2K