Answer:
m = 4.29 kg
Explanation:
Given that,
Mass of the object, m = 2.8 kg
Stretching in the spring, x = 0.018 m
Frequency of vibration, f = 3 Hz
Let m is the mass of the object that is attached to the spring. When it is attached the gravitational force is balanced by the force on spring. It is given by :
[tex]mg=kx[/tex]
[tex]k=\dfrac{mg}{x}[/tex]
[tex]k=\dfrac{2.8\times 9.8}{0.018}[/tex]
k = 1524.44 N/m
Since, [tex]\omega=\sqrt{\dfrac{k}{m}}[/tex]
[tex]m=\dfrac{k}{4\pi^2 f^2}[/tex]
[tex]m=\dfrac{1524.44}{4\pi^2 \times 3^2}[/tex]
m = 4.29 kg
So, the mass that is attached to this spring is 4.29 kg. Hence, this is the required solution.
