Α2. A simplified car model is shown in Figure A2. It travels horizontally at a constant speed of v = 30 miles per hour on a bumpy road (1 mile is approximately 1610 meters). The road surface is assumed to be rigid and has a sinusoidal profile shown in Figure A2. Both masses m and M vibrate only in the vertical direction. m=50kg, M = 1000 kg, k = 1,000,000 N/m x 1 m k M 3k 1 m 10.04 m Figure A2. (a) What is the vertical motion imposed onto the bottom spring by the road? [3] (b) Sketch the free-body diagrams for this base-excited vibration problem and derive the equations of motion for the vertical vibration of the system. [7] (e) Determine the displacements of m and M, and then the maximum acceleration of [12] (d) Determine the maximum force transmitted to M from the ground. [3] m.
Α2. A simplified car model is shown in Figure A2. It travels horizontally at a constant speed of v = 30 miles per hour on a bumpy road (1 mile is approximately 1610 meters). The road surface is assumed to be rigid and has a sinusoidal profile shown in Figure A2. Both masses m and M vibrate only in the vertical direction. m=50kg, M = 1000 kg, k = 1,000,000 N/m x 1 m k M 3k 1 m 10.04 m Figure A2. (a) What is the vertical motion imposed onto the bottom spring by the road? [3] (b) Sketch the free-body diagrams for this base-excited vibration problem and derive the equations of motion for the vertical vibration of the system. [7] (e) Determine the displacements of m and M, and then the maximum acceleration of [12] (d) Determine the maximum force transmitted to M from the ground. [3] m.
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