Simple Pendulum - Maximum Speed

[mparsons06]

1. Homework Statement :

A simple pendulum has a mass of 0.25 kg and a length of 1.0 m. It is displaced through an angle of 5.0° and then released.

1. What is the maximum speed?

2. What is the maximum angular acceleration?
Answer: 0.855 rad/s²

3. What is the maximum restoring force?
Answer: 0.214 N2. The attempt at a solution:

I got numbers 2 and 3 right, but I can't figure out number 1.

Here's my attempt:

m*g*L*sin $$\theta$$ = 1/2 *m*v²
(0.250)*(9.81)*(1.0)*(sin 5) = 1/2 * (0.250)*v²
0.124 = (0.125)v²
v² = 1.712 = 1.31 m/s

It is incorrect. Can someone please help me as to where I went wrong?

 

[rock.freak667]

You are equating a force to energy.

First draw a free body diagram and find the potential energy when it is displaced at 5°.

 

[mparsons06]

I drew the diagram, but I'm not sure how to find the potential energy?

 

[rock.freak667]

I drew the diagram, but I'm not sure how to find the potential energy?

From the lowest point to where it is displaced, what is the vertical height?