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