Oscillation in a hole through the Earth (hole is offset)

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The discussion focuses on calculating the period of oscillation for an object in a hole through the Earth that is offset from the center. The key equation used is derived from the simple harmonic motion and Newton's gravitational force principles. It is concluded that the period of oscillation remains the same as if the tunnel were through the center of the Earth. This conclusion is affirmed by participants in the discussion. The findings highlight the consistency of oscillation periods regardless of the tunnel's position.
Carbon123
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1. The problem statement, all variables and given/known
There is an Earth but the hole is not in the middle but the side.find the period of oscillation

Homework Equations


Simple harmonic equation.Newton gravitational force

The Attempt at a Solution


I got GMx/R^3+acc=0 so period of osciilations is the same as when tunnel is through the center is it correct ?(that the period is the same as in the center of the earth)
 
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WinstonC said:
so period of osciilations is the same as when tunnel is through the center is it correct ?
Yes.
 
Thanks
 
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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