Devise two damping mechanisms for these coupled pendulums

[LCSphysicist]

Homework Statement

Devise two damping mechanism.

Relevant Equations

All below

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I am not sure how i could begin, someone can help me?

In the first mode we have a spring not stretched, while in the second, is not only stretched but the balls are outing of phase by 180 ° too.

 

[haruspex]

Damping the oscillation of the spring is pretty easy, no?
Allowing free out of phase movement, but damping in-phase is trickier. Maybe start with a mechanism that would only permit out of phase motion, then see how to relax that to a merely frictional constraint.

 

[anuttarasammyak]

Lagrangean
$$L=\frac{1}{2}m_a \dot{\psi_a}^2 + \frac{1}{2}m_b \dot{\psi_b}^2 - \frac{1}{2}k(\psi_a-\psi_b)^2$$
would determine the motion but it does not show friction or damping.

 

[haruspex]

Lagrangean
$$L=\frac{1}{2}m_a \dot{\psi_a}^2 + \frac{1}{2}m_b \dot{\psi_b}^2 - \frac{1}{2}k(\psi_a-\psi_b)^2$$
would determine the motion but it does not show friction or damping.

Lovely, but of no help at all in answering this question.