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A mass hanging on a spring is given a positive initial velocity, V from equilibrium. The ensuing displacement, x = x(t), is governed by mx''= -ax | x'| - kx; x(0) = 0, x' (0) = V where x is displacement, -ax |x ' | is a nonlinear damping force, and kx is a linear restoring force.
(a) Given that the units of x and t are length and time, what are the units of m, k, a?
(b) What are the possible time scales and on which physical processes are they based?
(c) Assume the restoring force is small compared to the damping force. Non-dimensionalize the model using appropriate time and spatial scales (i.e., such that the remaining parameter appears in the (non-dimensional) restoring term.)
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Find all the solutions for b equals the zero vector - Apply elimination and back substitution and write the LU factorization of the system. use b=Lc and c=Ux to solve the system.
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According to the contemporary philosopher Ned Block, the doctrine of Functionalism in philosophy of mind is "guilty of liberalism". Could someone please provide a premise-by-premise reconstruction of his argument(s), specifically his famous "Nation o..
Write a paragraph describing your interpretation when the slope is positive, zero, and negative. If you were buying a home in this particular city, which slope would be most attractive to you and why?
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Probability. A grab bag contains 10 $1 prizes, 7 $5 prizes, and 5 $20 prizes. Three prizes are chosen at random. Find the following probabilities.
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