Given data
*The given mass of the ball is m = 0.400 kg
*The given height is h = 3.00 m
*The given spring constant is k = 600.0 N/m
*The value for the acceleration due to the gravity is
[tex]g=9.8\text{ m/s\textasciicircum{}2}[/tex]The expression for the spring compresses at a distance is given by the conservation of energy as
[tex]\begin{gathered} U_s=U_p \\ \text{mgh}=\frac{1}{2}kx^2 \\ x=\sqrt[]{\frac{2mgh}{k}} \end{gathered}[/tex]Substitute the values in the above expression as
[tex]\begin{gathered} x=\sqrt[]{\frac{2\times0.400\times9.8\times3.00}{600.0}} \\ =0.198\text{ m} \end{gathered}[/tex]