Obtaining system dynamic equation using Lagrangian 's approach?

Question

I have the following problem related to my thesis which is a 3dof mechanical system. In this system, there are two masses ($m_1,m_2$) that are linked with weightless two links ($l_1,l_2$). Two joints have consisted of spring-damper systems which can be rotated around the y-axis ($\theta_1,\theta_2$). The total system can be rotated around the x-axis ($\omega$) at the point of the origin of the cartesian plane. In order to derive the dynamic equation for the system, how can I obtain the potential and kinetic energies?

3-dof mechanical system