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Can someone help me explain this paradox please.
A simple harmonic oscillator $ma=-kx$ is a system that oscillates in one dimension. But the text book says one-dimensional system can't oscillate. Why is that?? Thank you in advance.

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    I suspect you are quoting the text out of context. Perhaps you could supply more detail, or a link.2012-06-28
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    There's no detail. The really short section of the textbook just says one dimensional system can't oscillate. And the question use the simple harmonic oscillator ma= -kx to state that it oscillate in one dimension and just asks to explain the paradox. Thanks2012-06-28
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    If all the book does is say, "a one-dimensional system can't oscillate" then there is no paradox - the book is just wrong. But I'd really like to see what it says myself before I make any judgement on it.2012-06-28
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    Perhaps "one-dimensional" is used in two different senses here. The harmonic oscillator is two-dimensional in the sense that $a$ is the second derivative of $x$, giving you two constants of integration to work with.2012-06-28

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