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How to get max velocity for simple pendulum

  1. Jan 31, 2013 #1
    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 [itex]\theta = 0.0800 \cdot cos[4.43t + \phi][/itex] find the maximum velocity


    2. Relevant equations
    [itex]\frac{1}{2}mv^2 = \frac{1}{2}kA^2[/itex]


    3. 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
     
    Last edited: Jan 31, 2013
  2. jcsd
  3. Feb 1, 2013 #2

    Simon Bridge

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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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