= Solution
A symmetric quadratic form has twice its off-diagonal entry as the coefficient of the mixed product. Comparing with the preceding <potential energy> and <kinetic energy> expressions gives
$$
\boxed{\mathbf V=mgl\begin{pmatrix}4&0\\0&1\end{pmatrix},\qquad \mathbf T=ml^2\begin{pmatrix}8&2\\2&1\end{pmatrix}.}
$$
Here $\mathbf V$ is the stiffness matrix and $\mathbf T$ the mass matrix in angular coordinates; their units differ accordingly. The dimensionless mass-matrix determinant is $8-4=4>0$ and its first diagonal entry is positive, so the <kinetic energy> is positive for every nonzero angular velocity.
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