A quarter car model of an automotive vehicle suspension system is shown in Figure Q2 below, where k₁ is the suspension stiffness, m, 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 = 22 kN/m, m₁ = 304.3 kg, k₂ = 82.2 kN/m, and m₂ = 36.1 kg. Give your answer to 3 sf. m1 Car mass Z k₁ Car spring Tire stiffness Figure Q2 Answer: m₂ Wheel mass

All values equal to 1

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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

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