Answer:
[tex]k = 12.136\,\frac{N}{m}[/tex]
Explanation:
The angular frequency of the system is:
[tex]\omega = \sqrt{\frac{k}{m} }[/tex]
The frequency is:
[tex]f = \frac{14\,osc}{11\,s}[/tex]
[tex]f = 1.272\,hz[/tex]
The angular frequency is:
[tex]\omega = 2\pi\cdot (1.272\,hz)[/tex]
[tex]\omega = 7.992\,\frac{rad}{s}[/tex]
The spring constant is:
[tex]k = \left(7.992\,\frac{rad}{s} \right)^{2}\cdot (0.190\,kg)[/tex]
[tex]k = 12.136\,\frac{N}{m}[/tex]
