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# Problems with Pendulums

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I have this problem. I''m trying to make a little pendulum swing back and forth. I''m trying to learn all this simple harmonic motion stuff off the ''net but I think I''m getting confused. Anyway, How would I go about making this pendulum swing back and forth around (0,5), it has a length of 13 and a mass of 1. I''d be most grateful for any help. Thanks Donuts

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Lets see...

Supposing all the weight is at the end of the pendulum, the angular acceleration is
g/r * the sine of the deviation from straight down.

So if you choose a starting angluar position & velocity, use this acceleration to keep working out it''s position/velocity.

If not all the weight is at the end, you get a smaller figure instead of g/r. Choose whatever number you want there, and see what it looks like. I think in reality, angular accel = torque / moment of intertia, where
Torque = force(which in this case is m*g*sin) * r, summed over all particles
Moment of inertia = m * r^2 summed over all particles.

Hope that makes sense.

Speaking of moment of inertia, I just got a new job, well an old job actually (better change my profile soon), collecting trolleys at a supermarket. I worked out the formula for a line of n trolleys:
I(n) = n*I(1) + (n^3-n) * m(1) * l^2
l (which I''d type as lambda if I bothered to change font) is the all-important property of the distance from one trolley to the next when they are joined up.

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the force equation is F=-kx

however, if you replace F by m*a=m*x', you get a diferencial equation which solves to : x=A*sin(sqrt(k/m)*t)

this is harmonic movement, now for the pendulum, the pendulum would only have harmonic movement if the amplitude is relatively small compared to the string length, so take that in consideration.
the k for a pendulum is k=m*g/l, where m is the mass of the weight at the end of the string, g is the gravitational acceleration, and l is the lengh of the string.

but remember, in order for it to be harmonic (so you could use the equations and get realistic results) you have to have A much smaller that l

so if you want to use this in 3d space :
Xx=Ax*sin(sqrt(g/l)*t)
Xy=Ay*sin(sqrt(g/l)*t)
Xz=Az*sin(sqrt(g/l)*t)

[edited by - danz on June 8, 2002 3:55:43 AM]

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I basically had what danz had but the movement I'm getting is back and forth in a diagonally instead of curved. How are Xx=Ax*sin(sqrt(g/l)*t) and Xy=Ay*sin(sqrt(g/l)*t)supposed to differ from each other.

[edited by - Donuts on June 8, 2002 9:21:38 PM]

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there is a different amplitude for each axis

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quote:
but remember, in order for it to be harmonic (so you could use the equations and get realistic results) you have to have A much smaller that l

What do you need to do if A is larger than l?

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if A is even half of l (not to mention bigger) then it is not a harmonic motion, and you should figure out another formula for the x(t) function, or else the simulation won''t be realistic

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