Why Can't SHM Explain a Ball Falling Through Earth's Radius?

AI Thread Summary
The discussion centers on the limitations of simple harmonic motion (SHM) in explaining the behavior of a ball falling through a hole in the Earth. It highlights that SHM is typically applicable for small displacements, where force is linearly proportional to displacement. However, in this scenario, the displacement is significant, potentially comparable to the Earth's radius, raising questions about the validity of the linear approximation. Participants emphasize that the standard model assumes uniform density and a small hole, which may not hold true for larger displacements. The conversation ultimately seeks to clarify the role of higher-order terms in the force equation when considering larger displacements.
Kolahal Bhattacharya
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We all know that a ball when dropped into a straight hole through the earth, it begins shm.The question I want to raise here is we know that SHM happens when displacement is very small so that F(x) depends only on the linear term kx and not on the higher order terms:x62, x63 etc.Here the displacement is very big, may well be compared to The Earth's radius.where I am going wrong?
 
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What higher order terms are you talking about? In the usual "ball dropped through a hole through the Earth" problem, we assume a uniform density and small hole, so that F(x) = kx throughout the motion.
 
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