The pipe carrying feed water to a boiler in a thermal power plant has been found to vibrate violently at a pump speed of $800$rpm$.$ In order to reduce the vibrations, an absorber consisting of a spring of stiffness k

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and a trial m

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mass of $1$ kg is attached to the pipe. This arrangement is found to give the natural frequency of the system as $750$rpm$.$ It is desired to keep the natural frequencies of the system outside the operating speed range of the pump, which is $700$rpm to $1040$rpm$.$ Determine the new values k

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and m

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that satisfy this requirement.