7.2. Derive the equations of motion for the three-degree-of-freedom system shown in Fig. 7.20 by means of Newton's second law. ks ke x1(t) x{t) x3(t) ki k2 ka ka m2 FIGURE 7.20 Three-degree-of-freedom system

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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.