The most the 'sin' of any angle can be is 1. At that time, d=8. / / / The least the 'sin' of an angle can be is -1. At that time, d=-8. / / / As 't' goes on, 'd' wiggles between -8 and +8. At equilibrium, d=0, and the amplitude of the wiggle is 8. That's also the maximum displacement from equilibrium.
