Use the law of conservation of energy.
Potential energy of the object with mass m at the height h is equal to:
E=mgh
and the potential energy of a spring is equal to Espring=1/2kx^2
where k = spring constant, x = displacement
Since all the gravitational potential energy will be transformed to the spring potential energy, its quite easy to figure out the displacement from this two equations
E= mgh
E= 29.80.2
E= 3.92
E=1/2kx^2
E=1/21225X^2
3.922=1225X^2
0.0064=X^2
X=0.08 m or 8 cm
