# 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).

XQ8L1P The Asker · Mechanical Engineering

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).
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).