Q$2)$ An $82-$kg machine tool is mounted on an elastic foundation. An experiment is run

to determine the stiffness and damping properties of the foundation. When the tool is

excited with a harmonic force of magnitude $8000$ N at various frequencies, the

maximum steady$-$state amplitude obtained is $4\mathrm{.}1$ mm at a frequency of $40$ Hz $.$

a$)$ Use this information to estimate the stiffness and damping ratio of the foundation

b$)$ Draw the graph of magnification factor vs frequency ratio, mark the peak and the $r$

in which peak occurs for all the damping factors you encounter in the problem and

comment on your observation.