How to get max velocity for simple pendulum

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SUMMARY

The maximum velocity of a simple pendulum with a mass of 5 kg and a string length of 5 m can be calculated using the formula v_max = ω * A * R, where ω is the angular frequency derived from the equation θ = 0.0800 * cos[4.43t + φ]. The angular frequency ω is determined to be 4.43 * 0.08, leading to a maximum velocity of 5 * 4.43 * 0.08. Understanding the relationship between displacement and velocity is crucial for solving such problems effectively.

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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 \\\\<br /> mv^2 = kA^2 \\\\<br /> v = \sqrt{\frac{kA^2}{m}} \\\\<br /> 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
 
Last edited:
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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.
 

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