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Simple Harmonic Motion Given Amplitude and Frequency

  1. Nov 20, 2016 #1
    1. The problem statement, all variables and given/known data
    A cheerleader waves her pom-pom in SHM with an amplitude of 17.3 cm and a frequency of 0.830 Hz .
    Find the maximum magnitude of the velocity.


    2. Relevant equations
    v = -w Asin(ωt+Φ) = -wx
    or
    Conservation of Energy:
    1/2kx2 + 1/2mv2 = 1/2kA2
    3. The attempt at a solution
    I tried v = -ω(x) using 0.173 as x
    v = -5.21(0.173) = -0.0901 > wrong

    I got the ω by solving for period T (1.205s), i then made this equal to 2π/ω to solve for omega.

    I have yet to try the conservation of energy. But what would be the x in this case?
     
  2. jcsd
  3. Nov 20, 2016 #2
    I just realized that i had an extra 0 there for -0.0901, should have been 0.901!
     
  4. Nov 20, 2016 #3

    ehild

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    Gold Member

    There are to many 0-s. And the magnitude is not negative!
     
  5. Nov 20, 2016 #4
    Thanks! :)
     
  6. Nov 20, 2016 #5
    I do have another question actually. How would i solve this?
    "Find the speed when the pom-pom's coordinate is x= 9.40 cm ."

    I tried to use the equation v = ωx and got 0. 48974, but i got the wrong answer
    v = (5.21rad/s)(0.094m) = 0.4897
     
  7. Nov 20, 2016 #6

    ehild

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    The velocity is the time derivative of the displacement. If x=Acos(ωt) what is v=dx/dt?
    V=ωA is the relation between maximum displacement and maximum speed.
     
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