Simple harmonic oscillation question

[sapiental]

the displacement of a simple harmonic oscillator versus time is
described by the function x = Asin(wt + phi)

find the speed when the displacement is sqrt(3) A/2

the answer is piA/2 but I have no idea how the professor got it...

the function for the velocity at point x in our book is

v_x_ = -wAsin(wt + phi)

for some reason it is hard for me to associate the position x with the speed... is there a formula that gives the velocity by just plugging in x?

I just also found a diagram that gives T = 2s which I didn't see before

 

[physics girl phd]

Hint -- Try to use conservation of energy.

 

[sapiental]

ohhhh right

v_x_ = +-w sqrt(A^2 - x^2)

I got it from here, thanks a lot!