Solve Spring Problem: 97.6g Ball Dropped from 58.7cm

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A 97.6 g ball is dropped from a height of 58.7 cm, compressing a spring by 4.60282 cm. The relevant equations used are mgh for gravitational potential energy and 0.5k(deltax)^2 for spring potential energy. The initial calculations converted units correctly, but the height used in the energy equation was incorrect. The correct height should include the spring compression, leading to the revised height of 58.7 cm plus 4.60282 cm. This adjustment results in the correct spring constant, k, calculated as 530 N/m.
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Homework Statement


A(n) 97.6 g ball is dropped from a height of
58.7 cm above a spring of negligible mass.
The ball compresses the spring to a maximum
displacement of 4.60282 cm.
The acceleration of gravity is 9.8 m/s2 :


Homework Equations


mgh
.5k(deltax)^2


The Attempt at a Solution


I first converted all grams to kg, and cm to m:
97.6g=.0976kg
58.7cm=.587m
4.60282cm=.0460282m
then:
mgh=.5k(deltax)^2
(.0976g)(9.8m/s^2)(.587m)=.5k(.0460282m)^2
k=530N/m

I really don't see what i could've done wrong, but this isn't the right answer, according to my homework service
 
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Hint: you took the wrong h.
 
lol, i forgot to add deltax to h
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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