Solve xi=omega/romega

$$\xi = \frac { \omega } { r \omega }$$

Solve for r

$$r=\frac{1}{\xi }$$

$$\xi \neq 0\text{ and }\omega \neq 0$$

Steps for Solving Linear Equation

Variable r cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by r\omega .

$$\xi r\omega =\omega$$

Reorder the terms.

$$r\xi \omega =\omega$$

The equation is in standard form.

$$\xi \omega r=\omega$$

Divide both sides by \xi \omega .

$$\frac{\xi \omega r}{\xi \omega }=\frac{\omega }{\xi \omega }$$

Dividing by \xi \omega undoes the multiplication by \xi \omega .

$$r=\frac{\omega }{\xi \omega }$$

Divide \omega by \xi \omega .

$$r=\frac{1}{\xi }$$

Variable r cannot be equal to 0.

$$r=\frac{1}{\xi }\text{, }r\neq 0$$

Solve for ξ

$$\xi =\frac{1}{r}$$

$$r\neq 0\text{ and }\omega \neq 0$$