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

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

Atrast m (complex solution)

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

Lineāra vienādojuma risināšanas darbības

Atņemiet \left(-m\right)\omega ^{2}x no abām pusēm.

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

Reiziniet -1 un -1, lai iegūtu 1.

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

Savelciet visus locekļus, kuros ir m.

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

Vienādojums ir standarta formā.

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

Daliet 0 ar \omega ^{2}x.

$$m=0$$

Atrast m

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

Lineāra vienādojuma risināšanas darbības

Atņemiet \left(-m\right)\omega ^{2}x no abām pusēm.

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

Reiziniet -1 un -1, lai iegūtu 1.

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

Savelciet visus locekļus, kuros ir m.

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

Vienādojums ir standarta formā.

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

Daliet 0 ar \omega ^{2}x.

$$m=0$$

Atrast t (complex solution)

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

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

Atrast t

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

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