แก้โจทย์ {l}{Mg+Ma-T=Ma_{r}}{T-mg-ma=ma_{r}}

$$\left\{ \begin{array} { l } { M g + M a - T = M a _ { r } } \\ { T - m g - m a = m a _ { r } } \end{array} \right.$$

หาค่า M, g, a, T, a_r, m (complex solution)

$$M=\frac{T}{a-a_{r}+g}\text{, }g=-a-a_{r}+\frac{T}{m}\text{, }a\in \mathrm{C}\text{, }T\neq 2a_{r}m\text{, }a_{r}\in \mathrm{C}\text{, }m\neq 0$$

$$M=0\text{, }g\neq a_{r}-a\text{, }a\in \mathrm{C}\text{, }T=0\text{, }a_{r}\in \mathrm{C}\text{, }m=0$$

$$M\in \mathrm{C}\text{, }g=-a\text{, }a\in \mathrm{C}\text{, }T=0\text{, }a_{r}=0\text{, }m\in \mathrm{C}$$

$$M\in \mathrm{C}\text{, }g=a_{r}-a\text{, }a\in \mathrm{C}\text{, }T=0\text{, }a_{r}\in \mathrm{C}\text{, }m=0$$

หาค่า M, g, a, T, a_r, m

$$M=\frac{T}{a-a_{r}+g}\text{, }g=-a-a_{r}+\frac{T}{m}\text{, }a\in \mathrm{R}\text{, }T\neq 2a_{r}m\text{, }a_{r}\in \mathrm{R}\text{, }m\neq 0$$

$$M=0\text{, }g\neq a_{r}-a\text{, }a\in \mathrm{R}\text{, }T=0\text{, }a_{r}\in \mathrm{R}\text{, }m=0$$

$$M\in \mathrm{R}\text{, }g=-a\text{, }a\in \mathrm{R}\text{, }T=0\text{, }a_{r}=0\text{, }m\in \mathrm{R}$$

$$M\in \mathrm{R}\text{, }g=a_{r}-a\text{, }a\in \mathrm{R}\text{, }T=0\text{, }a_{r}\in \mathrm{R}\text{, }m=0$$