Derive the equation of motion either by using Lagrange principle. Take m = 1kg, L = 1m, k₁= k₂=750N/m, c = 300 N-s/m, M = 2 kg. Determine the normal mode of vibration in this system.

Q.3. The normal modes of a three-DOF system with m₁= m₂= m₃ and k₁= k₂= k₃ are given as

Verify the orthogonal properties of these modes. If the system is given an initial displacement of

X =

and released, determine how much of each mode will be present in the free vibration. If the second mass is subjected to a forcing of , determine the resulting oscillation.