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Simple Harmonic Motion (displacement function)

  1. Dec 9, 2011 #1
    1. The problem statement, all variables and given/known data

    I learned that in simple harmonic motion,

    the displacement fuction is

    x(t) = A sin(ωt + Φ)

    or

    x(t) = A cos(ωt + Φ)

    but when do you use sine function or cosine function?

    can I use whatever I want whether a sine or cosine function?

    And what's that Φ in the equation?

    Is it a quantity called a phase angle??

    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 9, 2011 #2
    Note that cos(x) = sin(x + pi/2)
     
  4. Dec 9, 2011 #3

    ehild

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    Homework Helper
    Gold Member

    You can use both the sine and cosine functions for the displacement during SHM. You can call Φ phase angle or rather phase constant, and you can determine it form given initial conditions.
    If the SHM starts with maximum displacement the cosine function is convenient to use, as x=Acos(ωt) is maximum at t=0, so Φ=0.
    In the case when the SHM starts from zero displacement by giving the object some velocity, it is easier to use x=Asin(ωt).

    ehild
     
  5. Feb 26, 2012 #4
    A boby moves in S.H.M with a amplitude of 30mm and a frequency of 2.0Hz. Calulate the values of
    (a) the acceleration at the centre and extremeties.
    (b) the velocity at these positions
    (c) the velocity and acceleration of a point between the centre and extremity of the oscillation

    how would i approach a question like this?????....
     
    Last edited: Feb 26, 2012
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