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Answer:
The spring constant is approximately 46.382 newtons per meter.
Explanation:
From Physics, the period ([tex]T[/tex]), measured in seconds, experimented by an object under Simple Harmonic Motion:
[tex]T = 2\pi\cdot \sqrt{\frac{W}{g\cdot k} }[/tex] (1)
Where:
[tex]W[/tex] - Weight, measured in newtons.
[tex]g[/tex] - Gravitational acceleration, measured in meters per square second.
[tex]k[/tex] - Spring constant, measured in newtons per meter.
If we know that [tex]W = 127\,N[/tex], [tex]g = 9.807\,\frac{m}{s^{2}}[/tex] and [tex]T = 3.32\,s[/tex], then the spring constant of the system is:
[tex]\frac{T^{2}}{4\cdot \pi^{2}} = \frac{W}{g\cdot k}[/tex]
[tex]k = \frac{4\cdot \pi^{2}\cdot W}{g\cdot T^{2}}[/tex]
[tex]k \approx 46.382\,\frac{N}{m}[/tex]
The spring constant is approximately 46.382 newtons per meter.