Assuming pulleys and string are light, find the constraint equation for accelerations of $m_{1}$ and $m_{2}$ Solution $6 x_{1}+c+5 x_{2}+c^{\prime}=$ constant
$\Rightarrow \quad 6 \frac{d^{2} x_{1}}{d t^{2}}+5 \frac{d^{2} x_{2}}{d t^{2}}-0$
$\Rightarrow 6 a_{1}+5 a_{2}=0$