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Diagram
Diagram  
QUESTION: In the attached figure:

In (a), the spring is in rest.
In (b), a mass 'm' is hung from it and as a result it elongates 'e' amount and stays in equilibrium.
In (c), the 'm' mass is pulled downwards by 'x' distance and then let go. The mass will then execute simple harmonic motion with 'x' amplitude. But, my confusion is here:

In the book, it is written that "For the motion of the mass to be simple harmonic, the amplitude 'x' must be less than the elongation at equilibrium 'e', i.e. x<e"

I can't understand why this should be done. Can you help?

ANSWER: Otherwise, you end up in compression.  Most lab springs are not designed to be compressed.

---------- FOLLOW-UP ----------

QUESTION: I don't understand. Does this mean the spring will be deformed?

Answer
No, it means that you'll go past spring equilibrium (unstretched) during the oscillation.  Most springs which are used in physics labs are special and tapered to approximate Hook's "Law" of springs and behave in a non-linear ways when you try and compress them...in fact, the most common type I know naturally has its coils resting against one another.  If you bang the coils together, the experiment won't work, will it?

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Dr. Stephen O. Nelson

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I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.

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I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

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Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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