4.15 A model of a vehicle suspension system is given in Figure P4.15. Write the equations of motion in matrix form. Calculate the natural frequencies for k₁ = 10³ N/m, k2 = 104 N/m m₁ = 2000 kg, m₂ 50 kg. - k₂ Tire stiffness m Car mass k₁ Car spring M₂ Tire mass in 24h m m₂ k₂ x₁(0) -x₂(0) Figure P4.15 A two-degree-of-freedom model of a vehicle suspension 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.