Answer:
17.71N/m
Explanation:
The period of the spring is expressed according to the expression;
[tex]T = 2 \pi \sqrt{\frac{m}{k} } \\[/tex]
m is the mass of the object
k is the force constant
Given
m = 5.50kg
T = 3.50s
Substitute into the formula;
[tex]T = 2 \pi \sqrt{\frac{m}{k} } \\3.5 = 2 (3.14) \sqrt{\frac{5.5}{k} } \\3.5 = 6.28 \sqrt{\frac{5.5}{k} } \\\frac{3.5}{6.28} = \sqrt{\frac{5.5}{k} } \\0.557 = \sqrt{\frac{5.5}{k} } \\square \ both \ sides\\0.557^2 = (\sqrt{\frac{5.5}{k} })^2 \\0.3106 = \frac{5,5}{k}\\k = \frac{5.5}{0.3106}\\k = 17.71N/m[/tex]
Hence the force constant of the spring is 17.71N/m
