Mass-weighted coordinate ($q_i=\sqrt{m_i}{x}_i$)

For diagonal kinetic energy, $q_i=\sqrt{m_i}{x}_i$ changes the kinetic quadratic form to $\frac{1}{2}{\sum }_i{\dot{q}}_i^2$. The potential Hessian in these coordinates is $M^{-1/2}K{M}^{-1/2}$.