Pendulum with a spring attached

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    Pendulum Spring
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Homework Statement


Mass = 0.2 kg
Length of pendulum = 0.2 m
Force constant 3 n/m

Homework Equations



T = 2pi rad(m/k)
Sum of Torque

The Attempt at a Solution



I am really confused on where to start. I know you simply cannot plug it into the first equation listed above since all the mass isn't concentrated at the tip of the spring. I tried to find the distance the spring was compressed by attempting pythag, but that didn't work since I didn't have enough information. I attached the full question.
 

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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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