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A $3000$ kg machine tool exhibits a large resonance at $120$ Hz $.$ The plant manager attaches an absorber to the machine of $600$ kg tuned to $120$ Hz$.$

The new natural frequencies of the new system $($machine and absorber$)$ are: ${}_{n1}=Hz$ and ${}_{n2}=Hz.$

The frequencies at which the amplitude of the machine vibration with the absorber fitted is less than without the absorber ranges between ${}_1=,Hz$ and ${}_2=,Hz$; and greater than

${}_3=,Hz.$