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At what positions is the speed of a simple harmonic oscillator half its maximum? That is, what values of x / X give v = ±vmax/2 , where X is the amplitude of the

motion?

Hello, I am so confused about this question. I am not really sure where to start. Thank you so much!

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2 answers

  1. x = X sin w t
    v = X w cos w t

    so
    X w cos w t = (1/2) X w

    cos w t = 1/2

    w t = 60 degrees, 300 degrees etc
    or in radians pi/3 etc
    so what is x/X when wt = pi/3 etc
    x/X = sin wt
    x/X = sin 60, 300 etc
    x/X = .866 , -.866 etc

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  2. Oh, do cos wt = -1/2 as well

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