Simple Pendulum Problem: Solving for Amplitude without Small Angle Approximation

AI Thread Summary
To solve the simple pendulum problem with a length l and an amplitude of 45 degrees without using the small angle approximation, one must first determine the period of the pendulum using the formula T = 2π√(l/g), where g is the acceleration due to gravity. Additionally, calculating the third-harmonic content requires analyzing the pendulum's motion in terms of Fourier series to account for the non-linear effects of larger amplitudes. The challenge lies in accurately modeling the oscillation without simplifying sin(θ) to θ. Understanding the dynamics of the pendulum at larger angles is crucial for precise calculations. This problem emphasizes the importance of advanced techniques in physics for non-linear oscillations.
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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