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Unformatted text preview: position relative to the equilibrium point is a function of time t given by Ae-βt sin( αt + c ) for some positive constants A,α,β,c . (b) When an object falls in the presence of air resistence, its velocity is a function of time t given by mg b + Ce-bt/m , where m is the object’s mass, g is the gravitational acceleration near earth, and b is a positive constant. (c) When an object is given an initial velocity v upward from the earth, Newton’s gravita-tional law will show that the maximum height h that it reaches before returning to earth is related to v by r 2 GM ( h-R ) Rh , where G is the gravitational constant, M is the earth’s mass, and R is the earth’s radius. ——————————————————————-...
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