\[伝達率：T_R=\frac{|F_T|}{F}=\frac{A\sqrt{k^2+(c\omega)^2}}{m_u\cdot e\cdot\omega^2}\] \[\underline{\therefore 遠心力：F=m_u\cdot e\cdot\omega^2}\] \[ここで，\sqrt{k^2+(c\omega)^2}=k\sqrt{1+(\frac{c\omega}{k})^2}=k\sqrt{1+(\frac{c}{m}\cdot\frac{\omega}{k/m})^2}\\ =k\sqrt{1+(2\varepsilon\cdot\frac{\omega}{\omega_n^2})^2}=k\sqrt{1+(\frac{2\varepsilon}{\omega_n}\cdot\frac{\omega}{\omega_n})^2}=k\sqrt{1+(2\zeta Z)^2}\] \begin{align}ゆえに，T_R&=\frac{A\cdot k\sqrt{1+(2\zeta Z^2)}}{m_u\cdot e\cdot\omega^2}\\ &=\frac{(\frac{m_ue}{m})Z^2}{\sqrt{(1-Z^2)^2+(2\zeta Z)^2}}\cdot\frac{k\sqrt{1+(2\zeta Z)^2}}{m_u\cdot e\cdot \omega^2}\\ &=\frac{Z^2}{m}\cdot\frac{k}{\omega^2}\cdot\frac{\sqrt{1+(2\zeta Z^2)}}{\sqrt{(1-Z^2)^2+(2\zeta Z)^2}}\\ &=\frac{Z^2}{m}\cdot\frac{k}{\omega^2}\cdot\frac{\sqrt{1+(2\zeta Z)^2}}{\sqrt{(1-Z^2)^2}+(2\zeta Z)^2}\end{align} \[ここで，\frac{Z^2}{m}\cdot\frac{k}{ \omega^2 }=Z^2\cdot\frac{k}{m}\cdot\frac{1}{\omega^2}=Z^2\cdot\frac{\omega_n^2}{\omega^2}=\frac{\omega^2}{\omega_n^2}\cdot\frac{\omega_n^2}{\omega^2}=1\] \[\underline{\therefore T_R=\frac{\sqrt{1+(2\zeta Z)^2}}{\sqrt{(1-Z^2)^2+(2\zeta Z)^2}}}\]