Solved: A mass m is attached to the end of a spring whose constant is k. After the mass

Chapter 3, Problem 35

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A mass m is attached to the end of a spring whose constant is k. After the mass reaches equilibrium, its support begins to oscillate vertically about a horizontal line L according to a formula h(t). The value of h represents the distance in feet measured from L See FIGURE 3.8.21. (a) Determine the differential equation of motion if the entire system moves through a medium offering a damping force numerically equal to f3(dxldt). (b) Solve the differential equation in part (a) if the spring is stretched 4 feet by a weight of 16 pounds and f3 = 2, h(t) = 5 cos t, x(O) = x'(O) = 0. FIGURE 3.8.21 Oscillating support in 35

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