Mechanical Vibrations ME444
Problem Set 1
1. For the following systems derive the equation of motion in terms of the coordinates shown
in each figure. Also determine the natural frequency of the system.
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2. A 4OO-kg machine is placed at the midspan of a 3.2-m simply supported steel (E = 200
'>< 109 N/m I- beam. The machine is observed to vibrate with a natural frequency of 9.3
Hz. What is the moment of inertia of the beam's cross section about its neutral axis?
3. When a 2000-lb vehicle is empty, the static deflection of its suspension system
is measured as 0.8 in. What is the natural frequency of the vehicle when it is
carrying 700 lb of passengers and cargo?
4. A 50.kg pump is to be placed at the mid-span of a 2.8-m simply supported steel (E =200 x
109 N/m2) beam. The beam is of rectangular cross section of width 25 cm. What are the
allowable values of the cross-sectional height such that the natural frequency is outside
the range of 50 to 75 Hz?
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