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
Messages
2
Reaction score
0
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
 
Physics news on Phys.org
What do you have to look for?
 
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.
 
Thread 'Is 'Velocity of Transport' a Recognized Term in English Mechanics Literature?'

Thread 'Is 'Velocity of Transport' a Recognized Term in English Mechanics Literature?'

Here are two fragments from Banach's monograph in Mechanics I have never seen the term <<velocity of transport>> in English texts. Actually I have never seen this term being named somehow in English. This term has a name in Russian books. I looked through the original Banach's text in Polish and there is a Polish name for this term. It is a little bit surprising that the Polish name differs from the Russian one and also differs from this English translation. My question is: Is there...
View full post »

Thread 'Effect of mass on the acceleration of an elastic pendulum?'

I know that mass does not affect the acceleration in a simple pendulum undergoing SHM, but how does the mass on the spring that makes up the elastic pendulum affect its acceleration? Certainly, there must be a change due to the displacement from equilibrium caused by each differing mass? I am talking about finding the acceleration at a specific time on each trial with different masses and comparing them. How would they compare and why?
View full post »

Similar threads

I How does a large-angle pendulum oscillate?
Replies
7
Views
3K
A Modeling the damping of a physical rigid pendulum
Replies
1
Views
2K
I Solving for the Motion of a Spring Pendulum
2
Replies
76
Views
7K
Rolling Pendulum: Solving the Dynamics Equations
Replies
2
Views
3K
The period of a simple pendulum
Replies
20
Views
2K
Differential Equation of a Pendulum
Replies
32
Views
2K
Seeking advice on "simple" pendulum problem
Replies
27
Views
2K
Simple Harmonic Motion: Simple Pendulum
Replies
13
Views
3K
Difference between angular frecuency and velocity pendulum
Replies
5
Views
2K
Foucault Pendulum at the North Pole
Replies
9
Views
2K

Hot Threads

Recent Insights

Back
Top