SHM confusion

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?
 

Doc Al

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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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