Solve Pendulum Problem: Find Time Period

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Homework Help Overview

The discussion revolves around a problem involving a simple pendulum with a specified length and angular amplitude, where the goal is to find the time period of oscillation. The subject area is classical mechanics, specifically the dynamics of pendulum motion.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to apply the formula for the time period of a pendulum and expresses uncertainty about the relevance of angular amplitude. Some participants question the assumptions regarding the amplitude's effect on the motion being simple harmonic.

Discussion Status

Participants have engaged in clarifying the conditions under which the time period formula is applicable. There is acknowledgment of the original poster's calculations, and a conversion of radians to degrees has been discussed to validate the assumptions about amplitude.

Contextual Notes

The original poster indicates a lack of familiarity with the concepts involved and seeks guidance without direct answers. The discussion includes a note on the acceptable range of amplitude for simple harmonic motion.

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Homework Statement


This is not any school or any homework problem, It's just a problem I read in a book. And I don't know anything about it. So I would just like anyone to give me a brief guideline to solve this sum and please help me. (PS: don't tell me the answer, I want to try it on my own. Though I do need a lot of guidelines...)

I'm a real amateur, so you guys might find this sum easy, but i don't get it.
here it is:
A simple pendulum of length 40cm oscillates with an angular amplitude of 0.04 rad. Find the time period.


Homework Equations


[tex]T = 2 \pi \sqrt {L/g}[/tex]
(that's all I know... I don't know about rad)


The Attempt at a Solution


Well I did think about it and came to a conclusion that since the time period doesn't depend on the amplitude of the pendulum well the time period will be:
[tex]T = 2 \pi \sqrt {L/g}[/tex]
[tex]T = 2 * 3.14 \sqrt {0.4m/9.8}[/tex]
[tex]therefore T = approx. 1.26s[/tex]

Though I don't know what the answer is...
 
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The equation for the period of a simple pendulum is correct. However, it assumes that the amplitude of the pendulum's swing is not too great. It it gets too large, the motion is no longer simple harmonic. Most school books will allow an angle up to about 10 degrees as "small". The conversion of an angle in radians to degrees is given by 360 degrees is equivalent to 2 pi radians.
 
Umm...
Got it
when i converted the 0.04 rad into degree then I got it to be approx 2.29 degrees and since it is under 10 degrees as suggested by you my answer most probably is right and the motion is SHM.
Is it right?(I expect a yes though I will even accept a no too)
 
The answer is correct. :)
 
Yuhoooooooo!
Thanks for the help Stonebridge!
 

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