Timeline for Why does a simple pendulum or a spring-mass system show simple harmonic motion only for small amplitudes?
Current License: CC BY-SA 3.0
21 events
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| Feb 24, 2017 at 15:47 | comment | added | Ben | @MikeW, that's true, in the sense that where the response curve is smooth there will be some size of deformation which is small enough to be close enough to linear, but there is no guarantee that the size of deformation is big enough to be of interest for the problem at hand. That requires engineering. | |
| Feb 24, 2017 at 15:19 | comment | added | Yashas | Hooke's law itself is an approximation :) | |
| Feb 24, 2017 at 14:54 | comment | added | MikeW | @Ben I imagine there are physical laws that underpin the approximation that is Hooke's Law - in the sense that bulk properties of materials of a particular type are linear for "small" deformations - due to intermolecular/interatomic forces. | |
| S Feb 22, 2017 at 11:57 | history | suggested | MikeW | CC BY-SA 3.0 |
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| Feb 22, 2017 at 11:30 | review | Suggested edits | |||
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| Feb 22, 2017 at 5:08 | comment | added | Yashas | @krs013 For $\frac{\pi}{10}$, the approximation is accurate up to the second decimal place. I added a graph to clear things up. | |
| Feb 22, 2017 at 5:06 | history | edited | Yashas | CC BY-SA 3.0 |
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| Feb 22, 2017 at 1:07 | comment | added | krs013 | That's the first time I saw $\frac\pi{10}$ as a criterion for the small angle approximation. In fact, I've never seen any explicit limit for it at all. IMO, it's better to keep these things intentionally ambiguous so the answer to "how small is small enough?" is always "It depends; figure it out." | |
| Feb 21, 2017 at 18:59 | comment | added | Sierra | Also on further thought... I don't know why you put the L on the left in the acceleration equation... To make the acceleration linear instead of angular? But then wouldn't you have to do the same on the right...? The final equation has to be a=-gx/L, such x being the leg of the triangle in the original sin equation but becoming the arc in the small angle approximation but being cancelled out anyhow with the x of the SAM (not that it doesn't look confusing to me...). | |
| Feb 21, 2017 at 18:48 | comment | added | JMac | Just for the record, it's not really only under high strain that a spring doesn't obey Hooke's law. A spring never really follows Hooke's law perfectly. There is obviously some non-linear behavior in the spring anyways due to design, material inconsistencies, actual physical behaviour, etc. Springs also just happen to have very linear-elastic behaviour if properly designed and operated in the right range. The spring equation is approximate just like the pendulum equation though (especially since springs work because of shape, it's easy to imagine imperfections giving non-linear $k$). | |
| Feb 21, 2017 at 17:59 | history | edited | Yashas | CC BY-SA 3.0 |
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| Feb 21, 2017 at 17:47 | comment | added | Ben | @YashasSamaga, correct. Point: It's not a physical law in the same way as Newton's laws. You can buy nonlinear springs. | |
| Feb 21, 2017 at 17:37 | comment | added | Yashas | @Ben You can always go past the elastic limits and damage it. | |
| Feb 21, 2017 at 17:36 | history | edited | Yashas | CC BY-SA 3.0 |
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| Feb 21, 2017 at 17:06 | comment | added | Ben | Springs obey Hooke's law because, and to the extent that, they are carefully designed and manufactured to obey Hooke's law. | |
| Feb 21, 2017 at 16:14 | history | edited | Yashas | CC BY-SA 3.0 |
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| Feb 21, 2017 at 15:35 | history | edited | Yashas | CC BY-SA 3.0 |
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| Feb 21, 2017 at 13:54 | history | edited | Yashas | CC BY-SA 3.0 |
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| Feb 21, 2017 at 13:29 | vote | accept | whateven | ||
| Feb 21, 2017 at 13:26 | history | edited | Yashas | CC BY-SA 3.0 |
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| Feb 21, 2017 at 13:19 | history | answered | Yashas | CC BY-SA 3.0 |