Question $(3)$

The figure below is a sketch of a helicopter. The tail section of the helicopter can be idealized as a cantilever beam of length $l$ and bending rigidity $EI.$ The combined mass of the gear box and tail rotor blades is $50$ kg and is represented as a concentrated mass at the end of the cantilever, as shown. The natural frequency of the tail section is found to be $8$ Hz $.$ If one of the tail rotor blades suddenly falls off in flight, the remaining blades can be considered as an unbalanced rotating mass located at a distance of $150$ mm from the axis of rotation. If the blades rotate at $1200$ rpm $,$ determine the forced response of the tail section of the helicopter when one blade falls off. Assume the mass of one blade as $4$ kg and the equivalent viscous damping ratio of the tail section as $0\mathrm{.}15.$ Note that when a blode falls off, the mass at the end of the beam $($and thus its natural frequency$)$ changes.