Question

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!

Answer 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

Answer 2

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