(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A regular pendulum is swinging back and forth. Assuming it starts from a horizontal position, find an expression for its tangential velocity.

(I don't know if the question is posed right, I just asked myself it as a challenge)

2. The attempt at a solution

using a freebody diagram, I know that the tangential vector is the tangential component of weight. let Θ be the angle such that the tangential component of weight is mgsinΘ.

F = ma

mgsinΘ = ma

gsinΘ = dv/dt

I know im supposed to do

v = ∫gsinΘ dt

but I have no clue how to do that except using rotation equations,

Θ = α/2 t^2 + ωt = a/2r t^2 + v/r t = gcosΘ/2r t^2 + v/r t

which leaves me with messy algebra that brings me in circles...

can anyone help me set up this problem?

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# Derive velocity function for pendulum

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