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They certainly do sound periodic from observation. But is there a particular formula that proves that sound from Newton's Cradle is periodic?
I would think not since each end is half a pendulum. That assumption and a zero transit time for the impulse is all it takes to show it is simple harmonic motion. And even woth the delay it would still be periodic.I think of periodic as a uniform period. Isn't it the case that with Newton's Cradle the period decreases very slowly but constantly as the balls to go less and less high and return more and more quickly?
I thought the small amount of energy lost as heat due to the impact would change that. I guess your assumption of zero transit time makes it an ideal case with no lost energy so we are describing slightly different things, yes?I would think not since each end is half a pendulum. That assumption and a zero transit time for the impulse is all it takes to show it is simple harmonic motion. And even woth the delay it would still be periodic.
No, zero transit time is different from lost energy. With zero transit time you get a decaying amplitude sine wave (the decaying amplitude is the lost energy, whether it is in the impact or in air resistance). Including the transit time just gives you a little pause each cycle. This is why pendulums make good clocks: period is independent of amplitude.I thought the small amount of energy lost as heat due to the impact would change that. I guess your assumption of zero transit time makes it an ideal case with no lost energy so we are describing slightly different things, yes?
And this is why we need to be a bit more advanced and talk about differential equations.I thought the small amount of energy lost as heat due to the impact would change that. I guess your assumption of zero transit time makes it an ideal case with no lost energy so we are describing slightly different things, yes?
No, zero transit time is different from lost energy. With zero transit time you get a decaying amplitude sine wave (the decaying amplitude is the lost energy, whether it is in the impact or in air resistance). Including the transit time just gives you a little pause each cycle. This is why pendulums make good clocks: period is independent of amplitude.
Thanks guys.And this is why we need to be a bit more advanced and talk about differential equations.
In simple words, the friction would make a function that multiplies the sinusoidal function. No term from the friction will be present inside the sin function itself.
What this means: The period does not change, only the amplitude as russ_watters said.
But what proves that the sound is periodic? I'm not asking for the exact equation with exact values.@StevenJacobs990, the thread got a bit derailed by my misunderstanding but the answer is yes its periodic. As to the exact equation with exact values, that will depend on the parameters of the pendulum.
Would the period change depending upon the number of spheres in the cradle? I seem to hear 3 spheres in motion 'clanking' more frequently than when 5 are in motion?The period does not change, only the amplitude as russ_watters said.
... which is actually a function of the amplitude; not a strong function admittedly but still ....actually be half of the pendulum's
go less and less high and return more and more quickly
... , sorry Russ, but phinds was correct.period isindependent ofn amplitude.
We actually had a lab on the subject and I measured it again in some videos of newton's cradle. The frequency does not change, even if the masses were coupled in case of a symmetric motion (the two coupled masses move together in the same way).Would the period change depending upon the number of spheres in the cradle? I seem to hear 3 spheres in motion 'clanking' more frequently than when 5 are in motion?