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Simple Harmonic Motion amplitude problem

  1. Mar 1, 2014 #1
    1. The problem statement, all variables and given/known data

    An object is undergoing simple harmonic motion with frequency f = 3.1 Hz and an amplitude of 0.15 m. At t = 0.00 s the object is at x = 0.00 m. How long does it take the object to go from x = 0.00 m to x = 7.00×10-2 m.

    2. Relevant equations

    x(t)=Asin(ωt)

    3. The attempt at a solution

    The correct answer is 2.49*10-2sec

    ω=2[itex]\pi[/itex]f=6.2[itex]\pi[/itex]
    so, i set the following equation: 0.07=0.15sin(6.2[itex]\pi[/itex]t)
    but i can not solve it without the solving capabilities of a graphics calulator, so i cant use this method.

    i then set up a similar equation using small angle approximation but in order to get it to the right accuracy i need to include the second term (ie sinθ=θ - θ3/6
    but this then turns it into a cubic function (which i dont have the level of math to solve)

    Is there a different way to go about this question that i am missing?

    thank you in advance, Michael.
     
  2. jcsd
  3. Mar 1, 2014 #2

    ehild

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    Gold Member

    You need a simple scientific calculator only. What is sin(6.2πt)? With inverse sine, (and setting the calculator to radian mode), get the angle θ=6.2πt.

    ehild
     
  4. Mar 1, 2014 #3
    Thank you for the quick reply ehild.

    Wow, i cant believe i forgot about the inverse sine function on the normal calculators xD
    thanks alot!
     
  5. Mar 1, 2014 #4

    ehild

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    You are welcome:smile:

    ehild
     
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