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Simple Harmonic Motion

  1. Apr 21, 2015 #1
    1. The problem statement, all variables and given/known data
    My textbook states that for simple harmonic motion, the sinusoidal graph of the x (displacement) as a function of time can be created using the "Equation of motion".

    2. Relevant equations
    The equation of motion ##A \cos (\omega t + \phi)##

    3. The attempt at a solution
    I know that ##A## stretches the cosine graph vertically, but that the frequency is unaffected. How do ##\omega## and ##\phi## affect the graph?
     
  2. jcsd
  3. Apr 21, 2015 #2

    SammyS

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    Try some values and see.

    or ...

    What do you know about shifting and stretching/shrinking of graphs in general?

    What is the period of y = cos(x) ?

    How does the graph of y = f(x + k) compare with the graph of y = f(x) ?

    etc.
     
  4. Apr 22, 2015 #3
    Thank you so much! Is my understanding below valid?

    ##A## stretches/compresses the graph vertically
    ##\omega## affects the period. The larger ##\omega## is, the shorter the period.
    ##\phi## is the horizontal shift and it is negative. That is, a positive value of ##\phi## will shift the graph to the left.
     
  5. Apr 22, 2015 #4

    SammyS

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    Correct.
     
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