Answer:
Step-by-step explanation:
Using the formula for the ratio of period of damped motion to the period of undamped motion
[tex]\frac{Td}{T} = (1 - \frac{γ^{2} }{4km} )^{-1/2}[/tex]
[tex]\frac{140}{100} = (1 - \frac{γ^{2} }{4} ) ^{-1/2}[/tex]
[tex]\frac{7}{5} = (1 - \frac{γ^{2} }{4} ) ^{-1/2}[/tex]
Solving for damping coefficient γ,
[tex](\frac{5}{7})^{2} = 1 - \frac{γ^{2} }{4}[/tex]
[tex]0.5102 = 1 - \frac{γ^{2} }{4}[/tex]
[tex]γ^{2} = (1 - 0.5102) *4 \\[/tex]
γ = [tex]\sqrt{1.9592}[/tex] = 1.4
