Answer:
γ = 13 lb.s/ft
Step-by-step explanation:
Weight = 13 lb
L = 1.5 inches = 0.125 ft
To determine the value of γ for which the system is critically damped.
We write the general equation for such a system
my" + γy' + ky = 0
And this is critically damped when the roots are equal, that is
γ² - 4km = 0
k = spring constant = (weight/L) = (13/0.125) = 104 lb/ft
m = (w/g) = (13/32.2) = 0.404 lb.s²/ft
γ² - 4km = 0
γ² - 4(104)(0.404) = 0
γ² = 168.604
γ = 12.98 = 13 lb.s/ft
