Question

Creep +recovery (recoil) test on viscoelastic tissues We are considering: ơ(t)-Applying a load stress on a piece of tissue ! de(t) dt do(t) dt ODE: Hint: Read Ozkaya, Ch. 15.4, page 225 -227 before you attempt the problem below. Pay attention to Fig 15.11 (a), Fig 15.17, Fig 15.18, and try to understand the physics that he's talking about there !) 1) Using Laplace transforms, find the transfer function H (s)5 a(s) from the numerator of H (s) El ที่ from the deominator of H (s) Hint: If you factor out an: you will have a nicer H(s) to work with. And yes-the factored η terms will cancel out too so that's nice ! 2) Sketch the pole-zero plot of H(s). Indicate the locations of the poles and zeros in terms of the variables E, , E2 , and . For this sketch, you can assume E2 > E1 3) Using partial fractions, find the step response output strain (elongation) ε(t) when the input is a(t)u(t) 4) Suppose we vary the elastic modulus E2 from low values to high values a) On your pole-zero plot, indicate how the zeros and poles of H(s) will move b) How will your step response change as E2 increases ? Make a rough sketch on how ε(t) will change as you change E2. Then, in a sentence or two, explain what's happening with the total tissue elongation E(t) in terms of the biophysics of the problem Hint: Look at your tissue model in Figure 1. What will physically happen if E2 -» o?

Answer 1

dE と Applying laplace Trans ferm or @j σ(t) e uw ,. (s): σ.cs(-seeeee0-1 l+ω:

Et eit Eier. ETEL ,レ E incseases e the delat time decreaser. So thot nyt ¼ine, reat time an ancreases, onl get the 个 el t EL at to
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