$159$:

An aircraft engine has a rotating unbalanced mass $0\mathrm{.}06$ kg at radius $0\mathrm{.}06$ m $.$ If the wing can be modelled as a cantilever beam of uniform cross section a $b,$ 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 $t=5m,$ a $=0\mathrm{.}01m,b=0\mathrm{.}8m$ and the density and elastic modulus of the wing material as $=2700k\frac{g}{m^3}$ 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.