The kinetic energy for a three degree-of-freedom system is [ T=3left(dot{x}_{2}-frac{1}{2} dot{x}_{1} ight)^{2}+12left(dot{x}_{2}+frac{1}{3} dot{x}_{1} ight)^{2}+4 dot{x}_{3}^{2} ]

The kinetic energy for a three degree-of-freedom system is

\[ T=3\left(\dot{x}_{2}-\frac{1}{2} \dot{x}_{1}\right)^{2}+12\left(\dot{x}_{2}+\frac{1}{3} \dot{x}_{1}\right)^{2}+4 \dot{x}_{3}^{2} \]

Determine the mass matrix for the system.