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hmw11 - Due BME 171 Spring 2010 HOMEWORK#11 System Analysis...

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Due April 21, 2010 BME 171, Spring 2010 - HOMEWORK #11 System Analysis Using Laplace Transform: Vestibular Apparatus The vestibular apparatus is the organ responsible for the sense of equilibrium. It is located within the inner ear and consists of three semicircular canals connected to a common chamber called the utricle. In this assignment, we will concentrate on the mechanical performance of a semicircular canal, illustrated in the figures on p. 3. Please, study these figures before proceeding. The equation describing the motion of cupula is m d 2 γ dt 2 + r dt + k γ ( t ) = λm d 2 φ dt 2 (1) where γ ( t ) is the angular displacement of cupula from equilibrium φ ( t ) is the angular position of the skull m is the mass of the fluid plus cupula (inertia) r is the resistance to flow within the canal (damping) k is the effective restoring force per displacement of cupula (elasticity) λ = a/A is the ratio of cross-sectional areas of the canal ( a ) and the ampulla( A ) The numerical values are: k/r = 0 . 1 Hz, r/m
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