Question regarging pendulum axis and its motion

[callekula]

Hi,

I have a question regarding a pendulum and it's motion/momentum given the axis it moves around.

In the below picture, there are two version of a pendulum with a weight at the bottom. It moves in and out of the screen, around an axis resting on two nails (red). My question is, how does the distance (x and y) of the axis affect the motion, if we neglect the weight of the horisontal bar? Will the x-version move for a longer period of time, if the pendulum is released from the same position as the other version? Or is there no difference?

 

[BvU]

Hello callekula, !

In a physics forum you can expect a physics answer; in PF, however, we really value the input from the poster: what do you think ? And instead of a direct answer (a spoiler, so to say) you get guiding questions an little nudges to help you find the answers you are looking for.

To help you on your way: if you had to write down the equations of motion for these pendula, would your lengths appear in those ?

 

[callekula]

Hi BvU,

I appreaciate your willingness for me to figure it out myself. However, the pendulum I am building does not look like the ones in the school books with formulaes attached to them, there they are often depicted hanging in a string in one fixed point. This pendulum swings using this horisontal bar that rests on two screws, so I could never figure this out myself I think.

 

[BvU]

Seems to me you are able to do the experiment !
My reply was 'first order': pendulum moves in the z plane and your x and y don't appear in the equations of motion.
For an accurate clock mechanism you'd need a much more detailed description to estimate higher order effects (bending, friction, ...)

 

[callekula]

Sure, I'm not expecting to get an exact answer with such a simple problem description. My gut feeling, if the weight of the bar is neglected, is that it won't make any difference. But in my actual case it does have a weight, although very small (a wooden bar, 2 cm in diameter). So I'd be curious if it had a notable effect of the motion over a period of time, if this particular bar would be a factor say 6 times longer. I'd definitely do experiments, but was just reaching out if someone already knew :-)

 

[A.T.]

Will the x-version move for a longer period of time, if the pendulum is released from the same position as the other version?
View attachment 248152

If the longer bar bends more, it will dissipate energy quicker. The period might also be different due to that and the greater moment of inertia.