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Solve the following Problems. 1. If a Kelvin model system experiences a step displacement (x0) for a long time, what is the steady state force for each component of the model? That is, after the displacement is held for an indefinitely long time, what is the steady state force of the spring with stiffness k1, the spring with stiffness k0, and the dashpot with damping coefficient h0? 2. Based on the discussion for section 2.6.1, show the steps to derive equation 2.14 for a Kelvin model from page 56 of the Ethier and Simmons text. Provide a solution for the following steps to get to the final answer. a. Write an equation for the total displacement, in terms of each of the components b. Write the equations of force for each element, in terms of Ẋ (1st derivative) c. Write an equation for the total force (do any elements have the same force?) At this point, some substitution and rearranging should get you to the final solution. 3. From Ethier and Simmons, Section 2.10, Complete Exercises: 2.8, 2.9 Note for Exercise 2.8: Change these values for this problem! r0 = 25 mg/ml, A0 = 350 mm2 , and F = 650 x 10-9 N. Note for Exercise 2.9: b is called a “constant”, but it is a proportionality parameter that can clearly vary. Don’t let the term “constant” bother you, since your expression for b is to be dependent on bead position and time. For part b, change the following values: b = 225 nN mm, viscosity = 2.5 g/(cm s), and the diameter of the beads was a full 5 mm. Acceptable design specs are when experimental error is < 5%.

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