45. In order to design an underwater vehicle that has the characteristics of both a long-range transit vehicle(torpedo-like) and a highly maneuverable low-speed vehicle(boxlike), researchers have developed a thruster that

mimics that of squid jet locomotion (Krieg, 2008). It has been demonstrated there that the average normalized thrust due to a command step input, U (s)=Tref/s given by: T(t)=T_{r e f}\left(1-e^{-\lambda t}\right)+a \sin (2 \pi f t) where Tref is the reference or desired thrust, A is the system's damping constant, a is the amplitude of the oscillation caused by the pumping action of the actuator, f is the actuator frequency, and T(t) is the average resulting normalized thrust. Find the T(s)/U(s) . Show thruster's transfer function all steps.

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