For the record, here is the answer from the author itself in one of its articles:

The difficulty with traditional spring-damper models is that, if the contact-space inertia is too large the contact will be springy and result in large penetration and subsequent oscillation, while if the inertia is too small the dynamics will be stiff and very difficult to integrate numerically. Since the contact-space inertia is configuration-dependent while the spring-damper coefficients are fixed, this problem may seem unavoidable. However, if we have access to the diagonal of the ? matrix we can tune the spring-dampers online, and for example make sure that we always have critically-damped springs at all contacts.

From MuJoCo: A physics engine for model-based control

For the record, here is the answer from the author himself in one of his articles:

The difficulty with traditional spring-damper models is that, if the contact-space inertia is too large the contact will be springy and result in large penetration and subsequent oscillation, while if the inertia is too small the dynamics will be stiff and very difficult to integrate numerically. Since the contact-space inertia is configuration-dependent while the spring-damper coefficients are fixed, this problem may seem unavoidable. However, if we have access to the diagonal of the ? matrix we can tune the spring-dampers online, and for example make sure that we always have critically-damped springs at all contacts.

From MuJoCo: A physics engine for model-based control

For the record, here is the answer from the author itself in one of its articles:

The difficulty with traditional spring-damper models is that, if the contact-space inertia is too large the contact will be springy and result in large penetration and subsequent oscillation, while if the inertia is too small the dynamics will be stiff and very difficult to integrate numerically. Since the contact-space inertia is configuration-dependent while the spring-damper coefficients are fixed, this problem may seem unavoidable. However, if we have access to the diagonal of the ? matrix we can tune the spring-dampers online, and for example make sure that we always have critically-damped springs at all contacts.

From Implicit nonlinear complementarity: A new approach to contact dynamics

For the record, here is the answer from the author itself in one of its articles:

The difficulty with traditional spring-damper models is that, if the contact-space inertia is too large the contact will be springy and result in large penetration and subsequent oscillation, while if the inertia is too small the dynamics will be stiff and very difficult to integrate numerically. Since the contact-space inertia is configuration-dependent while the spring-damper coefficients are fixed, this problem may seem unavoidable. However, if we have access to the diagonal of the ? matrix we can tune the spring-dampers online, and for example make sure that we always have critically-damped springs at all contacts.

From MuJoCo: A physics engine for model-based control