The x-t graph of a particle undergoing simple harmonic motion is shown below.  The equation of the particle is given by

The equation of simple harmonic motion is given by $x=A\sin \left(\omega t+\varphi \right)$ . Using the  value of A = 1 cm and   $\omega =\frac{2\pi }{T}=\frac{2\pi }{8}=\frac{\pi }{4}$, we get $x=1\sin \left(\frac{\pi }{4}t\right)$