Simple Pendulum Problem: Solving for Amplitude without Small Angle Approximation

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SUMMARY

The discussion focuses on solving the simple pendulum problem for a pendulum of length l oscillating with an amplitude of 45 degrees, specifically without using the small angle approximation. Key tasks include calculating the period of the pendulum and determining the approximate amount of third-harmonic content in the oscillation. Participants emphasize the importance of considering the full sine function for accurate results, rather than the linear approximation.

PREREQUISITES
  • Understanding of simple harmonic motion
  • Familiarity with pendulum dynamics
  • Knowledge of Fourier series for harmonic analysis
  • Ability to apply trigonometric functions in physics
NEXT STEPS
  • Research the formula for the period of a simple pendulum without small angle approximation
  • Learn about Fourier analysis to calculate harmonic content in oscillations
  • Explore the effects of amplitude on pendulum motion
  • Study the mathematical derivation of pendulum motion equations
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Physics students, educators, and anyone interested in advanced pendulum dynamics and harmonic analysis.

einsteinian
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could you pleassee help me get started on this problem...im not sure how do it

1. A simple pendulum problem of length l oscillates with an amplitude of 45degrees. (Do it without the approx. of sin(theta) = theta)(small angle approx.)

any help would be awesome
 
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wow thanks i can't believe i forgot the most important part...the question

a) period?
b)find the approximate amount of third-harmonic content in the oscillation of the pendulum.
 

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