The following​ mass-and-spring system has stiffness matrix K. For the mks​ values, find the two natural frequencies of the system and describe its two natural modes of oscillation.   m1 m2 k1 k2 k3 x1 x2 K= −k1+k2 k2 k2 −k2+k3   m1=m2=4​; k1=8​, k2=12​, k3=8       Let ω1<ω2 be the two natural frequencies.

A quarter car model of an automotive vehicle suspension system is shown in Figure Q2 below, where ky is the suspension stiffness, my the sprung mass of a quarter of the vehicle, k₂ the tyre stiffness, and m₂ the unsprung mass, or wheel mass. Write the system equations of motion in matrix form, and hence find the first system natural frequency ie the lower value, in Hz. The system parameters are k₁ = 24.4 kN/m, m₁ = 257.5 kg, k₂ = 83.2 kN/m, and m₂ = 28.8 kg. Give your answer to 3 sf. m₁ Car mass 2 k₁ Car spring k₂ Tire stiffness Figure Q2 Answer: m₂ Wheel mass

Vibrations