Answer :
Explanation:
It is given that,
Mass of the block, m = 0.805 kg
Spring constant of a spring, k = 40 N/m
The mass moves in a fluid which offers a resistive force F = −b v, where b = 0.600 N⋅s/m
The angular frequency of oscillation is given by :
[tex]\omega=\sqrt{\dfrac{k}{m}-(\dfrac{b}{2m})^2}[/tex]
[tex]\omega=\sqrt{\dfrac{40\ N/m}{0.805\ kg}-(\dfrac{0.6\ N.s/m}{2(0.805\ kg)})^2}[/tex]
[tex]\omega=7.03\ rad/s[/tex]
The period of motion is T which is given by :
[tex]T=\dfrac{2\pi}{\omega}[/tex]
[tex]T=\dfrac{2\pi}{7.03}[/tex]
T = 0.89 seconds
So, the period of the motion of the block is 0.89 seconds. Hence, this is the required solution.