(Solved): The equation of motrin of a mass \( m \) relature to a cotating coorinate system is \[ \frac{m d^{ ...

The equation of motrin of a mass \( m \) relature to a cotating coorinate system is \[ \frac{m d^{2} r}{d t^{2}}=\vec{F}-m \omega \times(\omega \times r)-2 m\left(\omega \times \frac{d \vec{r}}{d t}\right)-m\left(\frac{d \omega}{d t} \times \vec{r}\right) \] Consider the case \( \vec{F}=0^{\circ}, \vec{r}=\hat{x} x+\hat{y} y \) and \( \vec{w}=\omega \hat{j} \). with \( w \) constant. show that the replacement of \( \vec{n}=\hat{x} x+\hat{y} y \) by \( \vec{z}=x+i y \) leads fo \( \frac{d^{2} z}{d t^{2}}+i 2 w d z-w^{2} z=0 \) This \( O \Delta E \) may be solved hy the silistitution of \( z=f e^{-c u t} \). \( z=f e^{-c u t} \)