Simple Harmonic Motion Pendulum

[sreya]

Homework Statement

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.

Homework Equations

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

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

$\sqrt(aL) = v$

 

[SammyS]

Homework Statement

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.

Homework Equations

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

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

$\sqrt(aL) = v$

Can you use Conservation of Energy ?

 

[goraemon]

From your title, I gather that this is a Simple Harmonic Motion (SHM) problem. If so, angle $\theta$ must be small. Also, the problem asks you to find the linear SPEED of the sphere, not the acceleration.

I would begin by reviewing the formulas for a simple pendulum, comparing them with the formulas for a solid pendulum, and seeing how such formulas are derived. Can you list some viable formulas?