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Simple harmonic motion

  1. Apr 20, 2012 #1
    1. The problem statement, all variables and given/known data

    An object is undergoing simple harmonic motion with frequency = 3.2 Hz and amplitude = 0.12 m. At = 0 the object is at = 0. How long does it take the object to go from = 0 to = 7.2×10−2 m?




    2. Relevant equations



    3. The attempt at a solution

    s(t)=Asin(ωt)

    A=amplitude=.12 m
    ω=2πf=2π*3.2=20.1
    t=undefined
    s(t)=.12sin(20.1)
    7.2*10^-2=.12sin(20.1t) divide out the .12
    .6=sin(20.1t) Take the inverse sin of both sides
    arcsin.6=20.1t The inverse of sin cancels out sin on the right so 20.1t is left.
    36.87=20.1t Divide out 47.75 to get t.
    t=1.8338 seconds

    They want the answer in two figs, I put 1.8, and they marked it wrong are my steps wrong?
     
  2. jcsd
  3. Apr 20, 2012 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    Your method is correct. But watch your units. The arcsin of .6 must be expressed in radians. You are using degrees.

    A good way to approach this kind of problem is to estimate it first. You can tell that it will be less than 1/4 of a cycle, and there are 3.2 cycles in one second, so it is a lot less than a second.

    AM
     
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