Question $4$

A machine $(1000$kg$)$ is designed to operate in the range of $1000$ to $5000$ rpm $.$ However,

the vibrations are observed to peak to an unacceptable level at a speed of $3000$ rpm $.$

a$.$ Design the vibration absorber $($i$.$e select dimensions, material, etc$)$

$($The correct final answer is E$=200$Gpa, d$=40$mm$,$ L$=0\mathrm{.}45$m$,$ M$=12\mathrm{.}07$kg$)$

b$.$ With the vibration absorber installed what critical speeds should be avoided?

$($The correct final answer is w$1=668\mathrm{.}1$rpm$,$ w$2=9354\mathrm{.}4$rpm$)$