A 20 kg computer system, used for data acquisition and data reduction in a laboratory, is...

 

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A 20 kg computer system, used for data acquisition and data reduction in a laboratory, is placed on a table which is bolted to the floor. Due to the operation of the surrounding rotating equipment, the floor has a vibration amplitude of 0.3 mm at a frequency of 35 Hz. The table can be modeled as a spring of stiffness 2 x 10 N/m with a damping ratio of 0.15. a) Determine the computer system's natural frequency, w, and frequency ratio, r. [CO2/PO3/C2] (4 marks) b) Find the steady state absolute displacement of the computer. c) Obtain the dynamic force on the computer system. [CO2/PO3/C4] (4 marks) [CO2/PO3/C4] (4 marks) d) What is the steady state acceleration amplitude of the computer system? [CO2/PO3/C4] (4 marks) e) Suggest one way to reduce the transmitted vibration amplitude to the computer system. [CO2/PO3/C4] (4 marks) B) In an experimental low frequency sound processing system, the 40 Hz frequency and its reflected harmonics up to 600Hz are to be removed from the recorded signal. Design a digital comb filter to meet these specifications. The design must include: a. A selection of an appropriate sampling frequency; [4 marks] b. An approximate sketch of the pole-zero diagram of the system; [6 marks] c. The computation of transfer function of the system; d. Computation of the difference equation of the system; [4 marks] [5 marks] e. Using computer tools like MS Excel, Google Sheets, MATLAB or any other appropriate tool, plot appropriate simulation graphs showing the filter meeting the required [10 marks] specifications. f. The 160 Hz frequency component is required to be studied for the experiment, modify the transfer function to include a resonator to allow this frequency to pass through the [6 marks] filter. A 20 kg computer system, used for data acquisition and data reduction in a laboratory, is placed on a table which is bolted to the floor. Due to the operation of the surrounding rotating equipment, the floor has a vibration amplitude of 0.3 mm at a frequency of 35 Hz. The table can be modeled as a spring of stiffness 2 x 10 N/m with a damping ratio of 0.15. a) Determine the computer system's natural frequency, w, and frequency ratio, r. [CO2/PO3/C2] (4 marks) b) Find the steady state absolute displacement of the computer. c) Obtain the dynamic force on the computer system. [CO2/PO3/C4] (4 marks) [CO2/PO3/C4] (4 marks) d) What is the steady state acceleration amplitude of the computer system? [CO2/PO3/C4] (4 marks) e) Suggest one way to reduce the transmitted vibration amplitude to the computer system. [CO2/PO3/C4] (4 marks) B) In an experimental low frequency sound processing system, the 40 Hz frequency and its reflected harmonics up to 600Hz are to be removed from the recorded signal. Design a digital comb filter to meet these specifications. The design must include: a. A selection of an appropriate sampling frequency; [4 marks] b. An approximate sketch of the pole-zero diagram of the system; [6 marks] c. The computation of transfer function of the system; d. Computation of the difference equation of the system; [4 marks] [5 marks] e. Using computer tools like MS Excel, Google Sheets, MATLAB or any other appropriate tool, plot appropriate simulation graphs showing the filter meeting the required [10 marks] specifications. f. The 160 Hz frequency component is required to be studied for the experiment, modify the transfer function to include a resonator to allow this frequency to pass through the [6 marks] filter.