(1 pcint) A mass weighing 4 lb stretches a spring 3 in Suppose the mass is dspla
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Question
(1 pcint) A mass weighing 4 lb stretches a spring 3 in Suppose the mass is dsplaced an additional 5 in in the pasitve (cownward) direction and then released with an initial upward velccity of 4 ft/s The mass Is in a medum, that exerts a viscuouse resistance of 4 lb when the mass has a velocity of 2 ft/s Assume g 32 ft/s is the gravitational acceleration (a) Find the mass ( in lb sft) (tb) Find the damping coefficient c in Ib s/ft 16 ” ) set up a differential equation that describes thls systern. Letto denote the displacement, n meters or the mass from its equilibrium position and give your answer in terms otZ, 1x'42x'+16x:0 (e) Enter the initial conditions: (00416667 z(0)0 (01:111s.isiallialdt11k.igxal,.r.iauix:iM 4:1:idly ilinr KHT? iti ft S ft/s Iin101ernfKXExplanation / Answer
Ans
x'(0) = -4 ft/s
Notice in the problem down direction is chosen as positive and mass is given velocity in up direcition i.e negative direction, hence the minus sign.
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