$5\mathrm{.}30$: A small rotating machine weighing $501$ b rus at a constant speed of $6000$ rpm $.$ The machine was installed in a building, and it was discovered that the system was operating at resonance. Design a retrofit undamped absorber such that the nearest resonance is at least $20\%$ away from the driving freqnency.

Solution:

By observing figure $5\mathrm{.}15,$ the values of $=0\mathrm{.}25$ and $=1$ results in the combined system's natural freqnencies being $28\mathrm{.}1\%$ above the driving frequency and $21\mathrm{.}8\%$ below the driving frequency $($since $=\frac{{}_a}{{}_p}=1$ and $={}_P).$ So$,$ the absorber should weigh

$m_a=m=0\mathrm{.}2550lb=12\mathrm{.}5lb$

and have stiffers,

$k_a=m_a{}_a^2=m_a{}^2$

$=12\mathrm{.}5164\mathrm{.}448222\frac{(N)}{1b}\frac{1}{9\mathrm{.}81}(\frac{60002i^2}{60}{)}^2$

$=2\mathrm{.}24{10}^6\frac{N}{m}$

$=12,800\frac{h}{i}n.$