Show that for a system with both viscous and Coulomb damping the approximate value of the steady-state amplitude is given by

\[X^{2}\left[k^{2}\left(1-r^{2}\right)^{2}+c^{2} \omega^{2}\right]+X \frac{8 \mu N c \omega}{\pi}+\left(\frac{16 \mu^{2} N^{2}}{\pi^{2}}-F_{0}^{2}\right)=0\]