In the system shown in Fig., AB is a massless rod which pivots freely about a pin connection at A. If the generalized coordinates are selected to be the angular orientation of the rod and the displacement of the second mass, obtain the differential equations of this system using Lagrange's equation. Use the assumption of small oscillations. B. m1 A k2 m2

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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.