A two degrees of freedom system, shown in Figure 2, has mass m1 equal to 1.0 kg, mass m2 equal to 0.1 kg, the spring stiffness k equals 100 N/m and the length l equals 0.1 m. Determine the natural frequencies of the system using Lagrange’s equations.

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Free undamped vibrations

Whenever an object/system displaces in either side of its equilibrium position with the help of an external/internal means, then the object/system moves regularly or randomly on both sides of its equilibrium position. This motion is called vibration. Generally, there are three types of vibration: longitudinal vibration, transverse vibration, and torsional vibration.