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Old Feb 19th 2019, 11:21 PM   #1
ohm
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SHM and oscillation

Give an example of oscillation which is not simple harmonic motion.
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Old Feb 20th 2019, 02:50 AM   #2
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Originally Posted by ohm View Post
Give an example of oscillation which is not simple harmonic motion.
I suppose we need to ask what do you mean by "oscillation?" Any periodic function would do the trick, I suspect. Howver if you want something more concrete than a function f(x+2) = f(x) then we can go with f(x) = sin( cos(x) ).

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Old Feb 20th 2019, 05:37 AM   #3
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To answer this, consider the assumptions that are made when considering SHM and then break those.

A pendulum where the initial position is very high and the small angle approximation does not hold.

A pendulum where the initial position is such that the string is slack (restoring force in the string interferes with the oscillation as well as aiding it).

A situation where the string/spring used to provide the restoring force has a low Young's modulus such that during the oscillation, permanent deformation in the string length occurs.

There are more...
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Old Feb 20th 2019, 07:02 AM   #4
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[QUOTE=topsquark;42651]I suppose we need to ask what do you mean by "oscillation?" Any periodic function would do the trick, I suspect. Howver if you want something more concrete than a function f(x+2) = f(x) then we can go with f(x) = sin( cos(x) ).
I read that simple harmonic motion is special case of oscillatory motion.. I want to know is there any example that in oscillatory motion but not in simple harmonic motion.
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Old Feb 20th 2019, 07:48 AM   #5
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SHM arises when there is a simple linear relationship between the displacement from the rest position and the strength of the action to restore conditions back to the rest position.

This is why "small" angles are specified for pendulums,
then the linear small angle approximation can be used.

If the restoration action is not a simple linear function of the displacement
then the oscillation will not be Simple Harmonic Motion.
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Old Feb 20th 2019, 09:56 AM   #6
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Originally Posted by ohm View Post
I read that simple harmonic motion is special case of oscillatory motion.. I want to know is there any example that in oscillatory motion but not in simple harmonic motion.
f(x) = sin( cos(x) ) is not a SHO. But Woody's example is better than mine.

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Old Feb 20th 2019, 11:18 PM   #7
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Any real life example
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Old Feb 21st 2019, 04:05 AM   #8
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One can come up with all kinds of weird and wonderful scenarios to force a non-SHM oscillation.

Perhaps a ball in a bowl.
The motion of a ball released from one rim such that it rolls down to the bottom of the bowl then back up toward the opposite rim, will not be necessarily be SHM; depending on the shape of the bowl.

However Benit's suggestion of a large angle pendulum is probably the most natural, the one that one is most likely to encounter in "real" life.
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Old Feb 21st 2019, 10:56 PM   #9
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Thanks
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