Answer:
[tex]-8<c<8[/tex]
Explanation:
Given data:
Weight W = 16 lb
length l = 6/12 = 0.5 ft
hence, spring constant k = W/l = 16/0.5 = 32 lb/ft
The equation of motion of spring is
[tex]mx''+cx+kx=0\\0.5x''+cx'+32x=0[/tex]
the auxiliary equation can be written as
[tex]0.5r^2+cr+32=0\\r^2+2cr+64=0[/tex]
The discriminate of equation is
[tex]D =(2c)^2+-4(1)(64)\\=4(c^2-64)[/tex]
To get the value of the damping constant,
[tex]D<0\\4(c^2-64)<0\\c>-8, c<8\\-8<c<8[/tex]
