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Unformatted text preview: t → ∞ . 4. Consider a spring/mass system held vertically, so that the mass also experiences a force due to gravity. Assume that the rest of the system, e.g., the spring and the damper, are essentially weightless. Since the spring is held vertically you might want to call the displacement y . (a) Determine the equation satis±ed by the displacement. (b) Determine a particular solution to the equation in terms of an undetermined coef±cient A . (c) Verify the units of the particular solution. 1 (d) Explain the physical signifcance oF the particular solution. (e) Make the transFormation z = y-A and determine the equation satisfed by the new variable z . (F) Explain the physical signifcance oF z and the equation that you Found. (g) Assuming c > so that there is damping, determine lim t →∞ y ( t ) . 2...
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- Spring '08
- initial conditions