Question $2(3$ points$)$

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An aircraft engine has a rotating unbalanced mass $0\mathrm{.}10$ kg at radius $0\mathrm{.}19$ m$.$ If the wing can be modelled as a cantilever beam of uniform cross section a x b$,$ as shown in the figure, determine the maximum deflection of the engine at a speed of $3000$ rpm$.$ Assume damping and the effect of the wing between the engine and the free end to be negligible. Give your answer in mm$.$ Take l $=5$ m$,$ a $=0\mathrm{.}01$ m$,$ b $=0\mathrm{.}5$ m and the density and elastic modulus of the wing material as $=2700$ kg$/$m$3$ and E $=72\mathrm{.}4$ GPa. Work to $3$ decimal places and do not include the units when submitting the answer. If your answer is a negative, insert it with the negative sign.