# Simple Harmonic Motion Pendulum

1. The problem statement, all variables and given/known data

A small sphere with mass m is attached to a massless rod of length L that is pivoted at the top, forming a simple pendulum. The pendulum is pulled to one side so that the rod is at an angle θ from the vertical, and released from rest.

When the pendulum rod is vertical, what is the linear speed of the sphere? Express your answer in terms of g, θ, L.

2. Relevant equations

$a = \frac{v^2}{r}$

3. The attempt at a solution

I’m not sure how to derive acceleration at this point. I know that

$mg-T=ma$

and that you could insert the acceleration derived here for the centripetal acceleration equation to derive velocity

But otherwise I’m kind of lost

$\sqrt(aL) = v$