Question

The pipe coming out of the pump is experiencing excessive vibrations. The pipe can be modeled as an SDOF system. The stiffness can be calculated by measuring the deflection (1 cm) when a force of 200 N is placed on the pipe. Additionally, a push test (pushing the pipe and letting it vibrate) showed that the natural frequency of the system is approximately 1 Hz. If the pipe vibrates at a frequency of 5 Hz during operation, design an undamped tuned absorber system considering that the absorber mass should not vibrate more than 1 mm.

          The pipe coming out of the pump is experiencing excessive vibrations. The pipe can be modeled as an SDOF system. The stiffness can be calculated by measuring the deflection (1 cm) when a force of 200 N is placed on the pipe. Additionally, a push test (pushing the pipe and letting it vibrate) showed that the natural frequency of the system is approximately 1 Hz. If the pipe vibrates at a frequency of 5 Hz during operation, design an undamped tuned absorber system considering that the absorber mass should not vibrate more than 1 mm.
        
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University Physics with Modern Physics
University Physics with Modern Physics
Hugh D. Young 14th Edition
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The pipe coming out of the pump is experiencing excessive vibrations. The pipe can be modeled as an SDOF system. The stiffness can be calculated by measuring the deflection (1 cm) when a force of 200 N is placed on the pipe. Additionally, a push test (pushing the pipe and letting it vibrate) showed that the natural frequency of the system is approximately 1 Hz. If the pipe vibrates at a frequency of 5 Hz during operation, design an undamped tuned absorber system considering that the absorber mass should not vibrate more than 1 mm.
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Transcript

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00:01 Hello students, here we need to find damping factor.
00:04 For that given volume mass 4 ton, then transient frequency which is damped frequency 7 .8 hz in radian per second it will be 2 pi into 7 .8 which is equal to 15 .6 pi radian per second.
00:30 Then the ratio of successive amplitude is given as a which is equal to 4 .5.
00:38 To find damping factor we have the formula delta is equal to lan of damping coefficient that is x naught by x1 which is ratio of successive amplitude that is the value of a.
00:59 From this we can write lan of a value 4 .5 which is equal to 2 pi damping factor gamma divided by root of 1 minus gamma square...
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