To solve this problem we will apply the concepts related to angular velocity as a function of the Period of a body. And with this angular velocity we will proceed to find the spring constant using the ratio of the mass and the square of the angular velocity. Our values are
[tex]T = 4s[/tex]
[tex]m = 2kg[/tex]
The angular frequency is defined as,
[tex]\omega = \frac{2\pi}{T}[/tex]
Replacing,
[tex]\omega = \frac{2\pi}{4}[/tex]
[tex]\omega = \frac{\pi}{2} rad /s[/tex]
Now the constant of the spring is defined as,
[tex]k = m\omega^2[/tex]
Replacing,
[tex]k = (2)(\frac{\pi}{2})^2[/tex]
[tex]k = \frac{\pi^2}{2}[/tex]
[tex]k = 4.93N/m[/tex]
Therefore the force constant of the spring used is 4.93N/m
