What is the deflection of a spring? a ball of mass 2kg is dropped from a height if 20cm on a spring of stiffness k=1225 n/m. find the maximum deflection of the spring.

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= 2*9.8*0.2
E= 3.92

E=1/2kx^2
E=1/2*1225*X^2
3.92*2=1225*X^2
0.0064=X^2
X=0.08 m or 8 cm