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# Lagrangian Dynamics - bead on wire watch

1. I have a bead on a wire that is at an angle to the vertical, I need to show that there is a starting distance along the wire where the bead will exhibit circular motion regardless of the radius.

Working in spherical polars I get the equation of motion as

mr''=mr(wsin(a))^2-mgcos(a)

which yields

r=A(e^wsin(a)t)-B(e^-wsin(a)t)+(gcos(a)/(wsin(a))^2)

I have been asked to show that for r0=gcos(a)/(wsin(a)) the particle exhibits circular motion. However, I get a hyperbolic function - which is correct for other starting conditions... and can't show that r'=0...

Any help appreciated. Thanks.
2. (Original post by natninja)
I have a bead on a wire that is at an angle to the vertical, I need to show that there is a starting distance along the wire where the bead will exhibit circular motion regardless of the radius.

Working in spherical polars I get the equation of motion as

mr''=mr(wsin(a))^2-mgcos(a)

which yields

r=A(e^wsin(a)t)-B(e^-wsin(a)t)+(gcos(a)/(wsin(a))^2)

I have been asked to show that for r0=gcos(a)/(wsin(a)) the particle exhibits circular motion. However, I get a hyperbolic function - which is correct for other starting conditions... and can't show that r'=0...

Any help appreciated. Thanks.
could you post the full question please? it's not clear to me what you mean/what the variables are.
3. (Original post by ben-smith)
could you post the full question please? it's not clear to me what you mean/what the variables are.
question 7b, think question is wrong and should be sin squared rather than sin as it works then.

EDIT attachment failed...
4. (Original post by ben-smith)
could you post the full question please? it's not clear to me what you mean/what the variables are.
here?
Attached Images
5. mech5 sheet.pdf (210.4 KB, 419 views)
6. (Original post by natninja)
here?
you are pretty much there. note that they gave you initial conditions.
7. (Original post by ben-smith)
you are pretty much there. note that they gave you initial conditions.
solved it - question was wrong... now stuck on 3c...
8. (Original post by natninja)
solved it - question was wrong... now stuck on 3c...
The trick is to notice that the second system is not inertial so you have to modify N2 when treating it.
9. (Original post by ben-smith)
The trick is to notice that the second system is not inertial so you have to modify N2 when treating it.
yeah got that didn't notice that T1=2T2 which made it come out in a few lines... but thanks

Though there is no way I can work out the potential function in 8b - using Divergence theorem maybe?

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