A mass attached to the free end of a spring executes simple harmonic motion according to the equation y = (0.50 m) sin (18π t) where y is in meters and t is seconds. What is the period of vibration?
not sure how to solve this, if someone would care to explain I would really appreciate it!! (answer is 1/9 sec)

The period T is defined as the smallest real T verifying : y(t+T) = y(t).

In your case, the motion is a sinus, which as you know verify the property : sin(u + 2*pi) = sin(u).

If you write u = 18*t, you obtain : sin(18*pi*t + 2*pi) = sin(18*pi*(t+1/9)).

Therefore : y(t+1/9) = y(t) which means that the period of vibration is 1/9 s