Question Solved1 Answer   right solution please In the figure below, the pipe carrying feed-water to a boiler in a thermal power plant "the pipe can be modeled as spring-mass system" has been found to vibrate violently at a pump speed of \( 427 \mathrm{rpm} \). If the operating speed range of the pump is between \( 360 \mathrm{rpm} \) to \( 900 \mathrm{rpm} \). In order to reduce the vibration, an absorber consisting of a spring of stiffness \( k_{2} \) and a trial mass of \( 10 \mathrm{~kg} \) is attached to the pipe and tuned to the \( 640.5 \mathrm{rpm} \) speed, i.e. tuning ratio of \( 1.5 \). This arrangement is found to give natural frequencies of the system at \( 342 \mathrm{rpm} \) and \( 800 \mathrm{rpm} \). Design the absorber to be attached to the pipe, i.e. calculating its mass \( \boldsymbol{m}_{2} \) and stiffness \( \boldsymbol{k}_{2} \) to satisfy the above-mentioned requirement ( to keep the natural frequencies of the system outside the operating range).

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right solution please

Transcribed Image Text: In the figure below, the pipe carrying feed-water to a boiler in a thermal power plant "the pipe can be modeled as spring-mass system" has been found to vibrate violently at a pump speed of \( 427 \mathrm{rpm} \). If the operating speed range of the pump is between \( 360 \mathrm{rpm} \) to \( 900 \mathrm{rpm} \). In order to reduce the vibration, an absorber consisting of a spring of stiffness \( k_{2} \) and a trial mass of \( 10 \mathrm{~kg} \) is attached to the pipe and tuned to the \( 640.5 \mathrm{rpm} \) speed, i.e. tuning ratio of \( 1.5 \). This arrangement is found to give natural frequencies of the system at \( 342 \mathrm{rpm} \) and \( 800 \mathrm{rpm} \). Design the absorber to be attached to the pipe, i.e. calculating its mass \( \boldsymbol{m}_{2} \) and stiffness \( \boldsymbol{k}_{2} \) to satisfy the above-mentioned requirement ( to keep the natural frequencies of the system outside the operating range).
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Transcribed Image Text: In the figure below, the pipe carrying feed-water to a boiler in a thermal power plant "the pipe can be modeled as spring-mass system" has been found to vibrate violently at a pump speed of \( 427 \mathrm{rpm} \). If the operating speed range of the pump is between \( 360 \mathrm{rpm} \) to \( 900 \mathrm{rpm} \). In order to reduce the vibration, an absorber consisting of a spring of stiffness \( k_{2} \) and a trial mass of \( 10 \mathrm{~kg} \) is attached to the pipe and tuned to the \( 640.5 \mathrm{rpm} \) speed, i.e. tuning ratio of \( 1.5 \). This arrangement is found to give natural frequencies of the system at \( 342 \mathrm{rpm} \) and \( 800 \mathrm{rpm} \). Design the absorber to be attached to the pipe, i.e. calculating its mass \( \boldsymbol{m}_{2} \) and stiffness \( \boldsymbol{k}_{2} \) to satisfy the above-mentioned requirement ( to keep the natural frequencies of the system outside the operating range).
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