Differential equation for unbalanced rotating force

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The differential equation presented is M\ddot{y} + k_{eq}y = me\omega^2\sin(\omega t), where M represents the total mass of the system. The discussion raises questions about the definition of m, whether it refers to the mass of the motor causing the unbalance or the entire system's mass. The lack of a figure complicates the understanding of the problem. Additionally, it is noted that the parameters of the ODE can vary across different physical systems, making it difficult to assign specific meanings without context. The conversation emphasizes the importance of clarity in defining variables in differential equations.
Dustinsfl
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Homework Statement


##M\ddot{y} + k_{eq}y = me\omega^2\sin(\omega t)##

What is ##m##?

Homework Equations

The Attempt at a Solution


In the ODE above, ##M## is the total mass of the problem, correct? For instance, if we had a cantilever beam, ##M = m_b + m_m(0.23)## where ##m_b## is the mass of the beam and ##m_m## is the mass of the motor.

Is ##m## the mass of the motor causing the unbalance or is it the mass of the whole system as well?
 
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Is there no figure associated with this problem?

To just start with the ODE given, I think that the only truly correct answer is to say that
m is the 13th letter of the alphabet.

The problem is that there are many physical systems that give rise to a particular describing differential equation. To start with the ODE and ask what the parameters are is pure nonsense.
 
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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