Answer:
10.23077 m
55.88391 N/m
Explanation:
m = Mass of person = 58.5 kg
T = Time period = [tex]\frac{45}{7}=6.42857\ s[/tex]
k = Spring constant
g = Acceleration due to gravity = 9.81 m/s²
Time period is given by
[tex]T=2\pi\sqrt{\frac{m}{k}}\\\Rightarrow T^2=4\pi^2\frac{m}{k}\\\Rightarrow k=\frac{4\pi^2m}{T^2}\\\Rightarrow k=\frac{4\pi^2 58.5}{6.42857^2}\\\Rightarrow k=55.88391\ N/m[/tex]
The spring stiffness constant is 55.88391 N/m
The force on spring is given by
[tex]mg=kx\\\Rightarrow x=\frac{mg}{k}\\\Rightarrow x=\frac{58.5\times 9.81}{55.88391}\\\Rightarrow x=10.26923\ m[/tex]
The unstreched length of the cord is 20.5-10.26923 = 10.23077 m
