Answer Happy

Question 2 (25 marks) a) A vehicle circulates on a road as shown in Figure Q2a. The road profile can be modelled as the input u(t). The vehicle is modelled as a quarter car of mass m, and the suspension has a spring stiffness coefficient k-2 Nm and a damper of coefficient c 2 Nm's. Find the position of the mass, ylt) and any time rif the road profile is a unit step. (10 marks) m He Road Figure Q2a b) In Figure Q2b, a disk flywheel of mass m = 32 kg and radius r = 0.5 m is driven by an electric motor that when it is working produces an oscillating torque of Tin = 10sin(wit) N- m. The shaft bearings may be modelled as viscous rotary dampers with a damping coefficient of Br= 0.4 N-m-s/rad and stiffness coefficient Ka= 2 Nm' of the flywheel is at rest at t = 0 and the power is suddenly applied to the motor, do the following (Hint: J = mrº/2]: (i) Find the natural frequency of oscillation of the disk expressed in Hz. [5 marks] (ii) Find the damping ratio for this system. [5 marks) (ii) Describe in no more than 3-4 lines the behaviour of the disk flywheel. [5 marks) bearing BR Flywheel Tino 32 Figure Q2b