Solve omega=sqrt{k/m}.

$$\omega = \sqrt { \frac { k } { m } } .$$

Solve for k

$$k=m\omega ^{2}$$

$$\omega \geq 0\text{ and }m\neq 0$$

Steps for Solving Radical Equations

Swap sides so that all variable terms are on the left hand side.

$$\sqrt{\frac{k}{m}}=\omega$$

Square both sides of the equation.

$$\frac{1}{m}k=\omega ^{2}$$

Divide both sides by m^{-1}.

$$\frac{\frac{1}{m}km}{1}=\frac{\omega ^{2}m}{1}$$

Dividing by m^{-1} undoes the multiplication by m^{-1}.

$$k=\frac{\omega ^{2}m}{1}$$

Divide \omega ^{2} by m^{-1}.

$$k=m\omega ^{2}$$

Solve for k (complex solution)

$$k=m\omega ^{2}$$

$$m\neq 0\text{ and }\left(\omega =0\text{ or }arg(\omega )<\pi \right)$$

Solve for m (complex solution)

$$\left\{\begin{matrix}m=\frac{k}{\omega ^{2}}\text{, }&k\neq 0\text{ and }arg(\omega )<\pi \text{ and }\omega \neq 0\\m\neq 0\text{, }&\omega =0\text{ and }k=0\end{matrix}\right.$$

Solve for m

$$\left\{\begin{matrix}m=\frac{k}{\omega ^{2}}\text{, }&\omega >0\text{ and }k\neq 0\\m\neq 0\text{, }&k=0\text{ and }\omega =0\end{matrix}\right.$$