Question

A precision machine is placed on a work bench. The ground vibration transmitted by a nearby internal combustion engine causes the base (bench) to vibrate at a frequency of 25 Hz with an amplitude of 0.6 cm. Design an isolation system to prevent ground motion to be transmitted to the precision machine, and at least 85% of vibration isolation must be achieved. If the machine has a mass of 48 kg, and the damper in the isolator has a damping constant of 950 N.s/m, 1) find the stiffness of the isolator, and 2) find the magnitude of the force transmitted to the machine. Must give the equation of the force transmitted to the machine and steps of finding its magnitude. Hint: check your free-body diagram for forces. a. Draw a mass-spring-damper diagram to represent this mechanical system. Label all necessary forces and displacements. Clearly indicate your sign convention. (10 points) b. Draw a free-body diagram of the machine consistent with your sign convention, and apply Newton's Law of Motion to derive the equation of motion consistent with your free-body diagram. (30 points) c. Show all steps of solving the equation of motion to reach your final answers. Directly using any transmissibility equation is not accepted. (40 points for 1) and 20 points for 2)

Answer 1

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As per HomeworkLib guidelines i have answered the first four parts of above problem.