Velocity, momentum and energy values for a Pendulum swing

[SpiraRoam]

Homework Statement

This is my 'carrying out a practical investigation' assignment for Maths. I've attached the coursework (what I've wrote up to now) and my main concern is whether I've got the right differential equation to find 3 new velocity values throughout the pendulum trajectory; quarter, mid, three quarters and 1 whole of the way throughout the first swing from being raised to an angle and let go.

The equation I've used I read from this wiki article (under 'energy derivation')
https://en.wikipedia.org/wiki/Pendulum_(mathematics)#math_Eq._1

The value that I have in the coursework seems way too large? That's why I think it may not be the right equation.

Cheers

Homework Equations

https://www.physicsforums.com/attachments/203521

https://www.physicsforums.com/attachments/203522

https://www.physicsforums.com/attachments/203524

The Attempt at a Solution

Once I've found all of the differential equations for angular velocity, momentum, kinetic and potential energy I can start to analyse the data with statistics and relate conclusions to my aims,hypothesis and theory.

I'm reading pages such as https://www.math.ucdavis.edu/~tracy/courses/math22B/22BBook.pdf to try and find the right equations but I am pressed for time with so much to do. Just thought I'd ask for help on here aswell. Thanks

 

[Eclair_de_XII]

The value that I have in the coursework seems way too large? That's why I think it may not be the right equation.

Those attachments do not work, by the way.

 

[Ray Vickson]

Homework Statement

This is my 'carrying out a practical investigation' assignment for Maths. I've attached the coursework (what I've wrote up to now) and my main concern is whether I've got the right differential equation to find 3 new velocity values throughout the pendulum trajectory; quarter, mid, three quarters and 1 whole of the way throughout the first swing from being raised to an angle and let go.

The equation I've used I read from this wiki article (under 'energy derivation')
https://en.wikipedia.org/wiki/Pendulum_(mathematics)#math_Eq._1

The value that I have in the coursework seems way too large? That's why I think it may not be the right equation.

Cheers

Homework Equations

https://www.physicsforums.com/attachments/203521

https://www.physicsforums.com/attachments/203522

https://www.physicsforums.com/attachments/203524

The Attempt at a Solution

Once I've found all of the differential equations for angular velocity, momentum, kinetic and potential energy I can start to analyse the data with statistics and relate conclusions to my aims,hypothesis and theory.

I'm reading pages such as https://www.math.ucdavis.edu/~tracy/courses/math22B/22BBook.pdf to try and find the right equations but I am pressed for time with so much to do. Just thought I'd ask for help on here aswell. Thanks

Type out your work if you really want help. Most helpers will not look at attachments, and even if they wanted to in your case they could not open them, and would instead find themselves in a digital black hole, requiring them to log out of PF and log in again to get back to the Forums.

 

[SpiraRoam]

Sorry for the late reply guys, I ended up solving it with derivatives and a vector notation function for circular displacement. Ended up being a bit of a jigsaw puzzle of finding values and plugging into the differential equations but I'm moving through the assignment now - thanks a lot.