File:Fixed-points theory and variance minimization (dynamic vibration absorber).png

${\displaystyle \left|{\frac {X_{m}}{x_{st}}}\right\vert ={\sqrt {\frac {(\alpha ^{2}-\beta ^{2})^{2}+(2\zeta _{a}\alpha \beta )^{2}}{\left[(\alpha ^{2}-\beta ^{2})(1-\beta ^{2})-\mu \alpha ^{2}\beta ^{2}\right]^{2}+(2\zeta _{a}\alpha \beta )^{2}(1-\beta ^{2}-\mu \beta ^{2})^{2}}}}}$

定点理論(Blue)、 ${\displaystyle \alpha _{opt}={\frac {1}{1+\mu }}}$、 ${\displaystyle \zeta _{a\ opt}={\sqrt {\frac {3\mu }{8(1+\mu )}}}}$

最小分散規範(Red)、 ${\displaystyle \alpha _{opt}={\frac {1}{1+\mu }}{\sqrt {\frac {2+\mu }{2}}}}$、

${\displaystyle \zeta _{a\ opt}={\sqrt {\frac {\mu (4+3\mu )}{8(1+\mu )(2+\mu )}}}}$