3. is A single degree of freedom model of a vehicle traveling at speed v over a rough road surface shown in Figure Q3(a). The vehicle has a mass of m = 880 kg, the suspension has a spring-damper system of a spring constant k = 400 kN/m and of a coefficient of viscous damping c = 3000 kg/s. The road surface varies harmonically (sinusoidally) with an amplitude Y = 1.5 cm and a wavelength (the length of one cycle) of 3.5 m. The behaviour of the vehicle can be investigated by using a base excitation model (see Figure Q3(b)). The vertical response (vibrations) x(t) of the vehicle are then governed by the second order differential equation of motion given as mx(t)+cx(t)+kx(t) = kY sin Qt+cY cost 1 2π ν where is the frequency of excitation due to the road surface given as ΩΞ 3.6 l where the speed v is expressed in km/h. a) Develop two models of the system: (i) MATLAB model (code) using a script file deploying a relevant ODE solver with m-function to represent the equation of motion (Q3); (ii) Simulink model (block diagram) to solve the equation of motion (Q3). (10 marks) b) Apply the models to simulate the dynamic response x(t) over the time interval [0, 20]s travels at two different speeds, 110 km/h and 45 km/h, respectively. when it (10 marks) c) Illustrate the results from the two models by plotting the vertical displacements of the vehicle as a function of time. (10 marks) d) Discuss the simulation results, explaining why the vehicle is subject to different vibration levels at the two speeds. (10 marks) y(t) m x(t) V (a) 771 x(t) y(t)-sint (b) Figure Q3. (a) Single degree of freedom model of a vehicle traveling over a rough road. (b) base vibration model.

Fig: 1