減衰振動

時刻 ${\displaystyle t}$ 〔s〕における物体の位置 ${\displaystyle x}$ 〔m〕，速度 ${\displaystyle v}$ 〔m/s〕

${\displaystyle x=A{e}^{-\gamma t}\cos ({\omega }^{\prime }t+{\theta }_0)}$

${\displaystyle v=-A{e}^{-\gamma t}\left\{\gamma \cos ({\omega }^{\prime }t+{\theta }_0)+{\omega }^{\prime }\sin ({\omega }^{\prime }t+{\theta }_0)\right\}}$

${\displaystyle {\omega }^{\prime }=\sqrt{{\omega }^2-{\gamma }^2}}$    ，      ${\displaystyle \omega =\sqrt{\frac{k}{m}}}$

${\displaystyle k}$ 〔N/m〕：ばね定数， ${\displaystyle m}$ 〔kg〕：物体の質量