Answer:
m = 3.91 kg
Explanation:
Given that,
Mass of the object, m = 3.74 kg
Stretching in the spring, x = 0.0161 m
The frequency of vibration, f = 3.84 Hz
When the object is suspended, the gravitational force is balanced by the spring force as :
[tex]mg=kx[/tex]
[tex]k=\dfrac{mg}{x}[/tex]
[tex]k=\dfrac{3.74\times 9.8}{0.0161}[/tex]
k = 2276.52 N/m
The frequency of vibration is given by :
[tex]f=\dfrac{1}{2\pi}\sqrt{\dfrac{k}{m}}[/tex]
[tex]m=\dfrac{k}{4\pi^2f^2}[/tex]
[tex]m=\dfrac{2276.52}{4\pi^2\times (3.84)^2}[/tex]
m = 3.91 kg
So, the mass of the object is 3.91 kg. Hence, this is the required solution.
