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Finding acceleration, velocity, and time for simple harmonic motion

  1. Apr 9, 2013 #1
    1. The problem statement, all variables and given/known data

    A cheerleader waves her pom-pom in simple harmonic motion with an amplitude of .180m and a frequency of .850Hz.

    a) Find the maximum magnitude of the acceleration and of the velocity.

    b) Find the acceleration and speed when the pom-pom's coordinate is x=+.090m.

    c) Find the time required to move from the equilibrium position directly to a point .120m away.

    d) Which of the quantities asked for in parts (a), (b), and (c) can be found using the energy approach (E = K + U = 1/2 mv^2 + mgh = 1/2 kA^2) and which cannot? Explain.


    2. Relevant equations

    i. x=Asin(ωt)

    ii. vx,max=ωA

    iii. ax,max=-ω2A

    where ω=angular frequency, A=amplitude, x=displacement from equilibrium, t=time

    K=1/2 mv^2

    U=mgh


    3. The attempt at a solution

    I was able to calculate (a) using formulas ii and iii. vmax=.961m/s; amax=5.13m/s^2

    I was also able to calculate (c) using formula i. x=7.16s

    However, I am unsure of how to find (b).

    I think (d) is velocity but I'm not sure if from velocity you'd be able to get x and acceleration?
     
  2. jcsd
  3. Apr 9, 2013 #2
    For part b you know ω, A, and x. You should be able to solve for and find t.

    I guess one way to solve "b" is by using your equation(i), you can find speed and acceleration by taking the 1st and 2nd derivative wrt t.
     
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