A spring with a K value of $200$ N$/$m is put vertically on the ground. You compress the spring

gradually and stop compressing at a force of $98$ newtons. Please calculate how much work is

done on the spring and how much potential energy is added to the spring. Now, instead of

compressing the spring, you put a $10$ kg weight on the spring and quickly released the weight

on top of the spring. What will happen to the spring; how the energy will be transferred

between the spring and weight? Will the spring be compressed more or less as compared to

the former case? What is the maximum potential energy will be added to the spring?