Hysteresis is a property that is unique to all the elastic products in which energy is lost during the recovery of the elastic from the stress it is put under. However, using the uncertainty for the value of acceleration 1. This result is closer to the value obtained in the graph. It also is to be noted that the point 0. Possible models of global warming: Changes in the composition of greenhouse gases in the atmosphere Increased solar flare activity.
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Share this Facebook. Amplitude and period relationship. Extracts from this document Bibliography "Harmonic oscillator -. Active 4 years, 1 month ago. Viewed 21k times. Improve this question. Noam Chai Noam Chai 1 1 gold badge 4 4 silver badges 15 15 bronze badges.
The only intuitive thing you can say is that the change is too small to observe. Add a comment. Active Oldest Votes. Improve this answer. JMac JMac When the angle is small the periodic bevaivour appears linear and approximately is , and this relationship only applies when it is linear.
Since it is only ever approximately linear, they are only approximately the same period. The higher velocity allows the higher pendulum to complete its swing in about the same amount of time as the lower, even though it has a longer path. The reason this works is that, for small perturbations the additional velocity is almost exactly the amount needed to account for the additional distance. For large perturbations, the additional velocity is not almost exactly that amount.
In real life, the assumption never holds; but it's close enough that for practical purposes you can say it does. In real life you also never get a massless string with a point mass suspended; so it falls apart for many reasons; that we can choose to ignore depending on how you formulate the problem.
Show 4 more comments. I think one of the important things to note about this is that near the end of the curve, the path looks approximately circular. That's one good semi-intuitive way to see how for small angles this applies to a pendulum. And a credit for henning would be appreciated Near that minimum, the height function and its second derivative can be exactly matched by a circle, and the first derivative vanishes, so you can get approximation accurate up to a 3rd-order error.
If the curve is left-right symmetric about the bottom point, then the error shrinks to 4th order. Show 3 more comments. Alfred Centauri Alfred Centauri The answers including the accepted answer that state the physical intuition is that there is higher potential energy at max displacement for larger amplitudes and thus higher kinetic energy at max velocity are wrong on my view; this intuition does not imply that the amplitude and period are independent.
He wanted "physical intuition" on why this works. This answer is entirely related to the differential equations, not the physics. Although I agree there are plenty of nuances to this question, i believe he accepted my answer because it was a simple physical explanation for why they can have the same period.
I purposefully avoided math and merely provided intuition on how it was possible from a physics school perspective. It seemed to be what the OP wanted more intuition about.
Also, it isn't true that my answer is entirely related to differential equations; the concepts of linearity and superposition are not limited to the context of differential equations. Indeed, I could remove the phrase "differential equation" from my answer as it isn't actually required. Show 7 more comments.
Enns M. The time for 50 oscillations was recorded for different lengths and angular amplitudes. It was observed that the period depends on length and angular amplitude of the pendulum. The variation of the period with the angular amplitude is not a linear relation, but a parabolic curve.
At the minimum values of the curves obtained, the angular amplitude can be between 5o to 15o for any choice of length of pendulum Keywords : Pendulum, period, oscillation, dependence, angular amplitude. Nigerian Journal of Physics Vol.
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