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 E spring = 1/2 k x^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