Answer
$\mu_s=0.788$
Work Step by Step
Static friction opposes the block's weight to prevent the block from slipping, so when the block does not slip, these two forces are balanced: $$f_s=W=(1.6kg)(9.8m/s^2)=15.68N$$ $$\mu_sF_N=15.68N$$
As the spring is pressed and the wall, as a result, is also pressed with increasing $F_x^{applied}$, the reaction (normal) force $F_N$ exerted back on the block by the wall also increases. According to Newton's 3rd law, $$F_N=F_x^{applied}=kx=510\times0.039=19.89N$$
Therefore, $$\mu_s=\frac{15.68}{F_N}=0.788$$
