Starting position on the cycloid. Can be greater than 0 (and less than \(2 \pi\)) . You mean, you still don't understand how this thing works? I think that you are confusing physics with religion, repeating the same mantra is part of the latter. How about you get working on writing the equations and finding out for yourself, eh? You had two weeks from when you opened the thread, you learned quite a few things, don't you think is time you stopped waiting for others to do your homework?
So you're claiming that the period of a cycloidal pendulum isn't independent of the initial amplitude? That is, the period "depends" on the initial angle between the cycloid and the pendulum? Or are you claiming that a rolling, not a sliding, ball in a cycloidal track isn't a cycloidal pendulum, it's "some other kind" of pendulum, whose motion depends on this angle? The first claim (if that's what you're making) is false: the period doesn't depend on the starting position, or the angle; it depends only on the radius of the generating circle. The second claim is also false: the rolling ball follows a cycoidal path so it will also have a period that depends on R, but also on the radius of gyration (another constant). Constant factors don't alter e.o.m. except by a constant factor.
You can't read , right? I posted the math that shows that the frictionless cycloidal pendulum has a period independent of the initial amplitude. I also posted the formula for the period of the rolling steel ball that shows the opposite to be true. ...for the rolling steel ball. Precisely. Now it is time for you to stop trolling for the math and to try deriving it yourself. If you can.
Now you're just lying. You've posted no math that "shows that the frictionless cycloidal pendulum has a period independent of the initial amplitude", and you haven't posted any math that "shows the opposite to be true" for a rolling steel ball. Unless, of course, you can point to a specific post where you have "posted the math". No?
I posted the formula for the period. How do you think I got that? Still trying to get someone else to show you how it's done? Tsk,tsk.
Are you sure you posted it in this thread? It's just, I can't see it anywhere. Where did you post the formula for the period of a rolling ball? You didn't post either formula did you? You are lying. But, you realise, it will be a very simple thing to prove me wrong about your lies: point to the specific posts. You realise that the original posts are still there, somewhere back in the thread, and since you "remember" posting the formulas, you shouldn't have any trouble finding them, unlike me. No?
You need to learn how to read. I even gave you the link about an hour ago. In this thread. You might have a learning disability, need to check that out. It is the second time you accused me of lying, time to have your face colored red.
So, no you can't post any reference to a specific post, because there aren't any posts containing these "formulas". So you are just a liar. You're so good at it it looks like you prefer lying to yourself as well, rather than admit you haven't posted what you're claiming you've posted? Amazing. And it's the second time you've failed to prove I'm wrong about your lies. Time to produce the links to the earlier posts with those formulas in them. No, you can't? Because they don't exist?
Don't get all twisted in your knickers, you even answered to the post. Reading disability? Search impaired?
Indeed. My answer indicated that I coudn't relate the first part of "the post" to the last part. You mention a "unrealistic" frictionless solution, but your solution isn't the formula for a period that looks like the one for a cycloidal pendulum. I can't see a formula in that post for a rolling ball pendulum either. You claim that a solution, using the integral you posted, for a rolling ball will be "much more complicated", and that's all you do. No formula that shows the period is independent of amplitude.
You have some very serious learning disability, I am sorry I can't help you with that. Can you try reading again. And again. And again. Until you comprehend? Must be tough being incapable to learn when you can't even read.
Remember this? And do you remember your original solution shows the period depends on the amplitude, which is wrong? Remember having to find a reason for the factor of 4 difference, between the actual working solution, and your original one?
What does your inability to understand the length of the cycloid pendulum have to do with your inability to find,read and understand the post explaining the period of the rolling steel ball? Don't you think that you could have made an attempt at this not so complicated problem in all this time you have been wasting trolling?
You've misunderstood this (again. I'm assuming you are purposely doing it now). The parameter \(\alpha\) does not vary from 0 to \(2 \pi\) with the equations I used for the cycloid, it varies from \(-\pi\) to \(\pi\). We've covered this ground before.
I understand the period of a cycloid pendulum just fine. My "inability" to find, read, and understand your explanation has an easy answer: you didn't explain anything. Furthermore, trying to get you to explain yourself is a really big waste of time. You are a waste of time. I see no point in engaging in any kind of discussion with you, except perhaps to ask how are your haemorrhoids. All anyone seems to be able to get out of you is your particular slant on what bullshit is.
Yes, you covered that in the post where you showed the plot for the cycloid, I answered that the correct thing to do is to invert the sign of y, not to change the equation for x combined with the change in parametrization. This is worse because you now have the arc length varying from -4R to +4R, so the arc length has become negative if you use that parametrization. In addition, the objection that your parametrization fails the computation based on energy conservation, stands.
And yet, the derivation of the equation of motion which includes the correct angular frequency, works perfectly with my method. You have still not provided this.
Yes, it does, doesn't change the fact that that you have a negative arc length. You haven't answered that. This is not an answer to the criticism, it is just a deflection. I could easily provide the equation of motion but I do not want to do arfa brane's homework especially since he's been insulting me with impunity right under your nose. So, I prefer to discuss the shortcomings in your derivation. So, how do you answer the criticisms to your approach?
This is simply a result of where I have defined the zero point to be. If you do the calculation correctly, by taking one side of the cycloid to be the negative direction and the other to be the positive you will presumably get the correct arc length. I genuinely don't believe you. It's not really much of a criticism. It follows from the solutions to the equations of motion that energy is conserved, so the fact that trying to work out the period by integrating over half a cycle doesn't work is the result of some subtlety that I haven't thought hard enough about.
The arc length is a monotonic function, so how do you plan to do the above? Do you have a justification for fiddling the signs? That is your problem , not mine. So, how about you work that out? Also, you mentioned that you will file an error report with Wolfram, how is that going? I do not see any change to accomodate your contention that they should change the parametrization for x to conform to yours.
