$4\mathrm{.}2$: A fixed$-$free beam of length $5$ m $,$ width $0\mathrm{.}25$ m $,$ thickness $($height$)0\mathrm{.}1$ m $,$ and elastic modulus of $209$ GPa $,$ carries an electric motor of mass $50$ kg and rotating at a speed of $1800$ rpm at its end as shown in Fig. $2.$ The rotor of the motor has an unbalanced mass of $2$ kg located $0\mathrm{.}05$ m from the axis of rotation. Find the amplitude of steady$-$state vibrations by disregarding the mass of the beam and assuming zero damping.

Fig. $2$