Given that the mass of the object is m = 1.2 kg
The coefficient of kinetic friction is given as
[tex]\mu_k=0.25[/tex]
The speed of the object is
[tex]v_i=\text{ 3.4 m/s}[/tex]
The force constant is
[tex]k=\text{ 50 N/m}[/tex]
We have to find the compression, d.
According to the conservation of energy
[tex]-\frac{1}{2}kd^2+\frac{1}{2}m(v_i)^2-\mu_kmgd=0[/tex]
Here, g = 9.8 m/s^2 is the acceleration due to gravity.
Substituting the values, the compression will be
[tex]\begin{gathered} -\frac{1}{2}\times50\times d^2+\frac{1}{2}\times1.2\times(3.4)^2-0.25\times1.2\times9.8\times d \\ -25d^2+6.936-2.94\text{d=0} \\ d=\text{ }0.471\text{ m} \end{gathered}[/tex]