Solve md^2x/dt^2=-momega^2x

$$m \frac { d ^ { 2 } x } { d t ^ { 2 } } = - m \omega ^ { 2 } x$$

Solve for m (complex solution)

$$\left\{\begin{matrix}\\m=0\text{, }&\text{unconditionally}\\m\in \mathrm{C}\text{, }&x=0\text{ or }\omega =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \left(-m\right)\omega ^{2}x from both sides.

$$m\frac{\mathrm{d}(x)}{\mathrm{d}t^{2}}-\left(-m\right)\omega ^{2}x=0$$

Multiply -1 and -1 to get 1.

$$m\frac{\mathrm{d}(x)}{\mathrm{d}t^{2}}+m\omega ^{2}x=0$$

Combine all terms containing m.

$$\left(\frac{\mathrm{d}(x)}{\mathrm{d}t^{2}}+\omega ^{2}x\right)m=0$$

The equation is in standard form.

$$x\omega ^{2}m=0$$

Divide 0 by \omega ^{2}x.

$$m=0$$

Solve for m

$$\left\{\begin{matrix}\\m=0\text{, }&\text{unconditionally}\\m\in \mathrm{R}\text{, }&x=0\text{ or }\omega =0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract \left(-m\right)\omega ^{2}x from both sides.

$$m\frac{\mathrm{d}(x)}{\mathrm{d}t^{2}}-\left(-m\right)\omega ^{2}x=0$$

Multiply -1 and -1 to get 1.

$$m\frac{\mathrm{d}(x)}{\mathrm{d}t^{2}}+m\omega ^{2}x=0$$

Combine all terms containing m.

$$\left(\frac{\mathrm{d}(x)}{\mathrm{d}t^{2}}+\omega ^{2}x\right)m=0$$

The equation is in standard form.

$$x\omega ^{2}m=0$$

Divide 0 by \omega ^{2}x.

$$m=0$$

Solve for t (complex solution)

$$t\in \mathrm{C}$$

$$x=0\text{ or }\omega =0\text{ or }m=0$$

Solve for t

$$t\in \mathrm{R}$$

$$x=0\text{ or }\omega =0\text{ or }m=0$$