Spring Potential/Work Energy Questions

Sasor

Question 1:

1. The problem statement, all variables and given/known data
You have a spring at height d where it is relaxed.
You drop a ball (mass m) from a height (h) so that it lands on the spring with spring constant k.
What is the max compression of the spring in terms of given variables?
Given-

m
g
k
d
h


2. Relevant equations
Find
dmax=max compression distance

3. The attempt at a solution
i did-

deltaUgrav+deltaUspring=0

(mg(d-dmax)-mg(d+h))+(.5k(dmax)^2-.5k(d-d))=0

mgd-mgdmax-mgd-mgh+.5k(dmax)^2=0

-mg(dmax)-mg(h)+.5k(dmax)^2=0

.5k(dmax)^2=mg(dmax+h)

Can you solve for dmax or do u have to do quadratic equation?


Question 2:

1. The problem statement, all variables and given/known data
If you have a spring and an object with mass m
and you put the object on the spring and let go, without giving it any initial velocity, what is the work done by the spring on the object? Answer is symbolic
Given variables-

Fspring with respect to s
m
g
k
s0(= initial length, relaxed length)
sf
2. Relevant equations

Symbollically, what is the work done?

3. The attempt at a solution

I did it like this-

Work= Integral(Fspring) evaluated from initial s to final s

so

Integral of ks ds= .5ks^2] sf-s0

=.5k(sf)^2-.5k(s0)^2
=.5k(sf-s0)

Is this the right amount of work?