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Homework Statement
A simple pendulum has a ball at the end of mass 5 kg and the length of the string is 5 m. Given [itex]\theta = 0.0800 \cdot cos[4.43t + \phi][/itex] find the maximum velocity
Homework Equations
[itex]\frac{1}{2}mv^2 = \frac{1}{2}kA^2[/itex]
The Attempt at a Solution
[itex]\frac{1}{2}mv^2 = \frac{1}{2}kA^2 \\\\
mv^2 = kA^2 \\\\
v = \sqrt{\frac{kA^2}{m}} \\\\
v = \omega \cdot A[/itex]
But the solution is [itex]v = \omega \cdot Length \cdot A[/itex]. 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
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