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Homework Help: Simple harmonic motion and frequency; answer disagrees from answer key

  1. Nov 24, 2008 #1
    1. The problem statement, all variables and given/known data

    A block attached to a spring oscillates in simple harmonic motion along the x axis. The limits of its motion are x = 10 cm and x = 50 cm and it goes from one of these extremes to the other in 0.25 s. Its amplitude and frequency are:

    A) 40 cm, 2 Hz
    B) 20 cm, 4 Hz
    C) 40 cm, 2 Hz
    D) 25 cm, 4 Hz
    E) 20 cm, 2 Hz


    2. Relevant equations

    [tex]T = 1/f[/tex]

    3. The attempt at a solution

    I got the amplitude correct by adding the limits and dividing by two to find the midpoint of the motion, which was 30 cm, which I took to be equilibrium. Then I subtracted 10 cm, one limit of motion, from 30 cm, equilibrium to get the amplitude of 20 cm.

    The frequency is where I mess up. I multiplied .25s by 2, since I thought it takes .25 seconds to complete half the cycle; I thought it must go back to the same extreme to complete a cycle, and thus would take another .25s. I got .5s for the period and then took the reciprocal of .5 for a frequency of 2 Hz.

    The answer key however says the answer is B, a frequency of 4 Hz. Is this a mistake of the answer key or on my part? I do not see why the frequency would be 4.
     
  2. jcsd
  3. Nov 24, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    I'd say that you are correct and the answer key is wrong.
     
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