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Hi,

If you suspend an object like a weightlifting bar (with 2 objects on both ends) in 2 places the same distance from the middle, when you spin the bar by puhsing one of the ends (so it rocks back and forwards, like a pendulum(?)), I assume, its the same, as though it had been suspended in the middle (yes?).

I've made a simple demo with this in, but I'm not sure my equations are right.. for instance, given the length of the bar, the distance the weights on both ends are from the middle, the mass of the weights, the distance the bar is suspended by the 'string' from the middle, and the force i send it rocking with.. how do you compute the time (assume bars mass is 0). Ive tried using pendulum laws, but Im not sure my method is correct :S

The way Ive programmed it isnt too solid either (only takes into account an acceleration for both ends).

As you probably noticed, my physics is not as up to scratch. Thanks.

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It is very unclear for me what you mean by "suspend." If you suspend rod in two points like that:


O----------.------.----------O


where dots is suspended points that is fixed, rod will be completely fixed and will not be able to rotate or move at all. That is, if rod moves, at least one of suspended points have to move.

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I'm sorry, for not being clear enough.


O----*--|--*----O


O, being the weights, | being the mid point, and the *'s representing pieces of string suspending the bar, in the air...


The problem is quite obtuse and I couldn't really find any resources on anything like this (best I got was pendulums). I want to know how long it takes for one swing when i provide a force on one end of the bar (rotating it around the center(?)). So in the diagram, that would be along the 'z' axis (not represented).


What sort of loss will there be in the time for a swing? I want to know how to program this right :)

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Ah, now I see what he means. That was a pretty confusing explanation, though. I think this (crude) ASCII drawing will clear it up:



========================================== ceiling
|
| |
| |
| |
| | <--- massless taut string
| |
| |
| |
| | massless rod
| | |
| | |
[][] | | | [][]
[][] | | v [][]
[][]========&===============&========[][] heavy weights
[][] ^ ^ [][]
[][] | | [][]
midpoint |
|
knots equidistant a specific distance r from midpoint

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Quote:
Original post by Genjix

I'm sorry, for not being clear enough.


O----*--|--*----O


O, being the weights, | being the mid point, and the *'s representing pieces of string suspending the bar, in the air...


The problem is quite obtuse and I couldn't really find any resources on anything like this (best I got was pendulums). I want to know how long it takes for one swing when i provide a force on one end of the bar (rotating it around the center(?)). So in the diagram, that would be along the 'z' axis (not represented).


What sort of loss will there be in the time for a swing? I want to know how to program this right :)


I think it's not the same as if you have only one string in the center.
If you have one string, it can rotate freely. If you have two, it can't.

As about simulation - this setup is nothing special and you can just simulate it as any mechanical system. Compute all forces acting on the rod (for strings and gravity, you can use old trick based on that their sum is orthogonal to string itself.), then acceleration of center of mass will be equal to sum of forces / total mass , and angular acceleration will be equal to sum of angular moments / inertia. (and inertia there is simply 2*M*r where M is mass and r is length of rod /2 , no need to work with inertia tensors or something)

There might be some "analitical" formulas for somewhat degenerate cases when strings is much longer than rod, or for case amplitude is very small, etc. But there's no analitical formulas even for pendulum that is at least somewhat accurate for big amplitudes.

edit:
i typed that reply before i seen kSquared's drawing. So i thought that your strings is connected to ceiling like that:

_________________________________________________
| |
| |
| |
| |
| |
| |
O-------------------------O

, but probably kSquared interpreted what you wrote more correctly.

In case them is connected in one point as on kSquared's drawing, and in case strings is always under tension, it is the same as if you have isosceles triangle with masses on the base vertices, and that can turn around upper point, or if you have kinda rigid string that always should have 90 degrees angle between rod and it.

Center of mass will move the same as pendulum. Turns the same as for any rigid body.

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:D



========================================== ceiling
| |
| |
| |
| |
| | <--- massless taut string
| |
| |
| |
| | massless rod
| | |
| | |
[][] | | | [][]
[][] | | v [][]
[][]========&===============&========[][] heavy weights
[][] ^ ^ [][]
[][] | | [][]
midpoint |
|
knots equidistant a specific distance r from midpoint

Originally I meant like this, but it also raises the question, whether both diagrams are equivalent (are they?).


So if you imagine the diagram representing the x,y plane and into the diagram representing the z plane. When I push the right heavy weight, what happens now? (obviously I know it'll make the bar spin anti-clockwise, till it slows and then reverses clockwise - swinging back and forth like a pendulum).


How long till it slows to a stop, how long till it reverses direction (on the first swing say), in terms of the Force I push it, the mass and distance from center on the right, (and where the bar is suspended with regards to the middle(??)).


Also when it slows down on first swing to change direction, what force is there on it causing it to change direction? Could I use this force in exactly the same way above (from the first swing), to see how long it takes from the change of direction, to the second change of direction (:P).


Sorry, for the lots of questions, its just really getting on my nerves (I couldnt find anything on the net)... and I really want to make this program.

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:D



========================================== ceiling
| |
| |
| |
| |
| | <--- massless taut string
| |
| |
| |
| | massless rod
| | |
| | |
[][] | | | [][]
[][] | | v [][]
[][]========&===============&========[][] heavy weights
[][] ^ ^ [][]
[][] | | [][]
midpoint |
|
knots equidistant a specific distance r from midpoint

Originally I meant like this, but it also raises the question, whether both diagrams are equivalent (are they?).


So if you imagine the diagram representing the x,y plane and into the diagram representing the z plane. When I push the right heavy weight, what happens now? (obviously I know it'll make the bar spin anti-clockwise, till it slows and then reverses clockwise - swinging back and forth like a pendulum).


How long till it slows to a stop, how long till it reverses direction (on the first swing say), in terms of the Force I push it, the mass and distance from center on the right, (and where the bar is suspended with regards to the middle(??)).


Also when it slows down on first swing to change direction, what force is there on it causing it to change direction? Could I use this force in exactly the same way above (from the first swing), to see how long it takes from the change of direction, to the second change of direction (:P).


Sorry, for the lots of questions, its just really getting on my nerves (I couldnt find anything on the net)... and I really want to make this program.

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So, my suggestions:

1: set-ups is very non-equivalent if amplitudes is not small.
2: there's aint no accurate analitical formulas even for pendulums at non-small amplitudes, and sure i can make analitical formula for case amplitude is very small, but it probably will not be so useful.
3: You probably need to simulate it numerically if amplitudes is not small.

Otherwise, i might be able to solve it for small amplitudes.

Actually it will not just turn back and forth, center of that thing will also move back and forth. Ratio of frequencies depends to rod length, string length, distance from center to string, etc.

(BTW. if amplitude is small, it look rather like homework.)

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I have one question about that...
What is initial configuration? Only one spring is streched? Both of them? Or one streched and second one another way around (sorry I couldn't find proper word).

I'm asking because... If only one is streched then rotation point is diffrent then middle point. If both of them are streched (in the same way) they will move only up and down and so on...

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Hi, I tried using pendulum formula's, but it yields contradictions. The best way I can think of to explain it, is to imagine this..


2 pieces of string hang from the ceiling, and attach it to a ruler (so the places where the string holds the ruler up, are the same distance from the center of the ruler. Now add to masses to both ends of the ruler.


Its been a long time since ive done mechanics, and cant really find the maths to explain it.


Thanks.

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