A 10kg block is immersed in a fluid which produces a resistive force to moving o

Question

A 10kg block is immersed in a fluid which produces a resistive force to moving objects of 3Nt for every 1 m/s. The block is hung vertically from a spring or spring constant k=2Nt/m which is firmly secured at another end. Once in equilibrium, the block is given an initial upward velocity of 1.5 m/s. Determine A) the differential equation for this system (don't forget initial conditions), B) If the system is over-damped, underdamped, or critically damped, C) its position function y(t) and D) the value of its velocity function y'(t) when t=1

Explanation / Answer

1)
mg=ky
k=mg/y
k=0.489*9.8/0.693=6.9 N/m

2)
F=-ky
a=-ky/m=-?^2y
?=(k/m)^1/2
?=(6.9/0.489)^1/2=3.76 rad/s
T=2?/?
T=3*3.14/3.76=1.67 s

3)
h=2A
A=0.353
h=2*0.353=0.706 m

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