Answer:
k = 543.9 N/m
Explanation:
Equation to Use:
[tex]T = 2\pi \sqrt{\frac{m}{k} }[/tex]
Knowns:
[tex]m = 0.31 kg[/tex]
[tex]T = 0.15s[/tex]
Rearrange Formula to solve for K (spring constant):
[tex]T = 2\pi \sqrt{\frac{m}{k} } \\\frac{T}{2\pi } = \sqrt{\frac{m}{k} } \\\frac{T^2}{4\pi ^2} = \frac{m}{k} \\k = \frac{m(4\pi ^2)}{T^2}[/tex]
Input Values and Solve:
[tex]k = \frac{0.31(4\pi ^2)}{0.15^2} \\k = 543.9 N/m[/tex]
k = 543.9 N/m
