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Simple harmonic motion of guitar string

  1. Nov 13, 2012 #1
    1. The problem statement, all variables and given/known data
    I have a question pertaining to the simple harmonic motion of the midpoint of a guitar string with a frequency of 4.40 x 10^2 Hz and an amplitude of 1.60 mm. I've been asked to deduce the initial displacement, velocity and acceleration of the midpoint of the string, but am a bit confused as to which equations I should be applying to find the answers.

    2. Relevant equations
    x (0) = A sin (phase constant). This is the equation for the initial displacement, but for the velocity I thought it would be Aw cos (wt + phase constant), but have come across another equation in my book that states velocity is Aw sin(wt + phase constant + Pi/2) ??

    Also it has been stated in the question that the phase constant is Pi/2 in this instance. Do I substitute the sine and cosine values for Pi/2 which are 1 and 0 respectively, in place of Pi/2. These figures are in the uniform circular motion part of my textbook, but do they also apply to the type of s.h.m in the question above?

    Any suggestions to point me in the right direction would be greatly appreciated!

    3. The attempt at a solution
  2. jcsd
  3. Nov 13, 2012 #2


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    2016 Award

    Staff: Mentor

    Re: s.h.m

    Aw cos (wt + phi) = Aw sin(wt + phi + Pi/2)
    Those are equivalent, as the cosine is just a sine shifted by pi/2.

    I don't understand that question.

    You can use the formulas for uniform circular motion, where just one component is your displacement and the other corresponds to the velocity.
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