Deriving the Equation for Period of Simple Pendulum? Is my attempt correct?

In summary, the conversation discusses deriving an equation with variables T, m, Theta, and l, where T is the period, m is the mass, Theta is the angle, and l is the length. The approach of considering the period as the perimeter of a circle is suggested. Various equations are then mentioned, such as C = 2pi r, t = sqrt(2pi r / (Ef/m)), and t = sqrt(2pi rm / sinTheta r). The idea of using the pendulum's arc and tangential component to prove simple harmonic motion and find the period is also mentioned. The person is unsure about using this method and asks for clarification.
  • #1
amd123
110
0

Homework Statement


I have to derive an equation with the following variables:
T= period
m= mass
Theta= angle
l= length

and I was told to think of the period as the perimeter of a circle.

Homework Equations


The Attempt at a Solution


[tex]C=2\pi r,C/2=\pi r,d=\pi r,(at^2)/2=\pi r,t=\sqrt{\frac{2\pi r}{Ef/m}},t=\sqrt{\frac{2\pi rm}{sin\Theta r }}[/tex]
 
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  • #2
It is simpler to just draw the pendulum's arc and then use then use the tangential component as the resultant force (F=ma).

This will help you prove that for small angles, the motion is simple harmonic and then the period will be easier to find.
 
  • #3
I have not come across any of the terminology you have just said.
I doubt I would be allowed to use that method.

Could you describe it in another way or comment on my attempt?
 

1. What is a simple pendulum?

A simple pendulum is a weight suspended from a fixed point that is able to swing back and forth under the influence of gravity.

2. What is the equation for the period of a simple pendulum?

The equation for the period of a simple pendulum is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity.

3. How is the equation for the period of a simple pendulum derived?

The equation for the period of a simple pendulum is derived using the principles of harmonic motion and the small angle approximation, assuming that the angle of displacement is less than 15 degrees.

4. Can the equation for the period of a simple pendulum be used for any length and mass?

Yes, the equation for the period of a simple pendulum can be used for any length and mass as long as the angle of displacement remains small and the acceleration due to gravity is constant.

5. How can I check if my attempt at deriving the equation for the period of a simple pendulum is correct?

You can check your attempt by comparing it to the accepted equation and making sure it follows the principles of harmonic motion and the small angle approximation. You can also ask for feedback from a peer or a mentor.

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