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

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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Damon 
Oh, do cos wt = 1/2 as well
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Damon
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