# How to get max velocity for simple pendulum

1. Jan 31, 2013

### PhizKid

1. The problem statement, all variables and given/known data
A simple pendulum has a ball at the end of mass 5 kg and the length of the string is 5 m. Given $\theta = 0.0800 \cdot cos[4.43t + \phi]$ find the maximum velocity

2. Relevant equations
$\frac{1}{2}mv^2 = \frac{1}{2}kA^2$

3. The attempt at a solution
$\frac{1}{2}mv^2 = \frac{1}{2}kA^2 \\\\ mv^2 = kA^2 \\\\ v = \sqrt{\frac{kA^2}{m}} \\\\ v = \omega \cdot A$

But the solution is $v = \omega \cdot Length \cdot A$. Why is it omega * the length * the amplitude?

EDIT: My friend helped me solve it:
w = dtheta / dt = -4.43*.08*sin(4.43t + phi)

w_max => 4.43t + phi = 3pi/2 => w_max = 4.43*.08

v_max = 4.43*.08*R = 5*4.43*.08

Last edited: Jan 31, 2013
2. Feb 1, 2013

### Simon Bridge

That's the one - it's what you get when you differentiate the displacement-time function: if you understand the displacement-time relationship you understand the velocity-time relationship.