Eng5932 - Sample Test 1 Questions 1. Consider a one degree of freedom model of a car. The car has mass 1500 kg and is designed for a passenger and cargo load of 750 kg. (a) The suspension should compress 3 cm when the design load (750 kg) is added to the vehicle, and the desired displacement transmissibility is 2 at resonance. Specify the spring constant, k, and damping constant, c, of the suspension system. (6 marks) (b) If the loaded vehicle travels at 100 km/h over a road that can be modelled as a sine wave of amplitude 4 cm and wavelength 10 m, determine the steady state response of the vehicle motion. (8 marks) (c) What is the amplitude of the force transmitted to the vehicle as it travels over the road surface speci…ed in part (b)? (3 marks) (d) If you could ‡ip a switch to adjust the suspension to improve passenger comfort on this road what would you adjust and how? Brie‡y explain how this adjustment would work. (3 marks) 2. A single cylinder air compressor of mass 100 kg is mounted on rubber mounts, as shown below. The e¤ective sti¤ness and damping constants of the rubber mounts are 1 MN/m and 2 kN s/m, respectively. The unbalance of the compressor is equivalent to a mass of 0.1 kg located at the end of the crank (point A), where r = 10 cm. If the compressor operates with a crank speed of 3500 rpm determine the steady state motion of the compressor. 3. A camcorder of mass m = 500 g is packed in a container using a ‡exible packing material. The sti¤ness and damping of the material are 1 kN/m and 20 N s/m, respectively. The container is dropped from an elevation of h = 2 m. Assume the container remains in contact with the ground after the drop and neglect the mass of the container and packaging when answering the following questions. (a) What is the motion, x(t), of the camcorder inside the container after it hits the ground? (b) Sketch the motion of the camcorder found in part (a), i.e. x(t) vs t. (c) If the camcorder can sustain an acceleration of 5g without damage, will it be damaged due to this drop? Eng5932 - Sample Test 1 Questions 4. A vertical take-o¤ and landing craft has a mass of 20,000 kg. As it lands it is supported by three struts, each of which consists of a linear spring and viscous damper. The spring constant for each spring is k = 130:8 kN/m and the damping constant of each damper is c = 23:6 kN s/m. Assume that when the vehicle lands the load is split evenly between all three struts. The vertical landing speed is x_ o = 0:5 m/s. (a) What is the equilibrium compression of the springs? (b) Assuming the springs are preloaded by 20 cm (i.e. before the vehicle touches the ground the springs are already compressed 20 cm), determine the vertical motion of the vehicle after landing. Choose x positive up. (c) Sketch (on x-! d t axes) the vertical motion of the vehicle after landing. (d) What is the ratio of amplitudes of oscillation measured over one full cycle? 5. Consider a crash barrier that is modelled as a spring and viscous damper. The linear spring constant of the barrier is k = 15 kN/m. The barrier is designed to give critical damping during impact with a 5000 kg vehicle. (a) If the 5000 kg vehicle impacts the barrier at 20 m/s, how far will it compress the barrier before it is stopped? (b) If a 1000 kg vehicle impacts the same barrier at 20 m/s, how far will it compress the barrier before it is stopped?