Consider the vibrations of a vehicle traveling forward at a constant speed on a road. The sprung mass of the vehicle is 750 kg and has a radius of gyration of 69.3 cm. The centre of mass of the vehicle is located 1 m from the front axle and 1.4 m from the rear axle. Each of the unsprung masses is 30 kg. The front and back suspension mechanisms are identical, each with elasticity of 18.25 kN/m and damping coefficient of 912.5 Ns/m. The front and back tires are identical, each with stiffness of 150 kN/m and negligible damping characteristics compared to those of the shock absorber.

Using a model with four degrees of freedom (pitch, bounce and wheel hops), compute the natural frequencies of the vehicle. Assuming a periodic road profile, calculate and plot the transmissibility of the bounce and pitch accelerations of the sprung mass in the frequency range between 0.1-30 Hz for traveling speeds of 25 km/h and 110 km.