Suppose the illustrated planar structure has unit masses at the nodes and the bars are all of

Question:

Suppose the illustrated planar structure has unit masses at the nodes and the bars are all of unit stiffness.

(a) Write down the system of differential equations that describes the dynamical vibrations of the structure.
(b) How many independent modes of vibration are there?
(c) Find numerical values for the vibrational frequencies.
(d) Describe what happens when the structure vibrates in each of the normal modes.
(e) Suppose the left-hand mass is displaced a unit horizontal distance. Determine the subsequent motion.