Problem deal with the mass-and-spring system shown in Fig. 5.4.11 with stiffness matrix -(k1 + k2) k2 k2 -(k2 + k3) K = and with the given mks values for the masses and spring con- stants. Find the two natural frequencies of the system and de- scribe its two natural modes of oscillation. k1 т k, k3 т, х1 FIGURE 5.4.11.

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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.