Q$1)$ A $150-kg$ electric motor has a rotating unbalance of $0\mathrm{.}5kg,0\mathrm{.}2m$ from the centre

of rotation.

a$)$ Assume the damping ratio as $0\mathrm{.}1,$ which will be the maximum allowable steady$-$

state amplitude of the system. What will be the frequency ratio this will happen

b$)$ Now keep the max steady state amplitude controlled within limits of $1$ mm $.$ The

motor is now kept on a simply supported beam of steel $(\{$:$E=210e+9\frac{N}{m^2})$ beam of

length $1$ m if the operating speed is $400$ to $1100$ rpm $.$ What should be the beam's

moment of inertia?

c$)$ What would happen if the damping factor is more than $0\mathrm{.}707?$