Upside Down Pendulum: Does Gravity Affect Its Tick Speed?

[gonegahgah]

Pendulums tick faster when they weigh more. ie a falling pendulum in any gravity won't tick as it is effectively weightless..

I was wondering if it were possible to make an upside down pendulum?

I've imagined that you could have an arm with a weight that is above the pivot point instead of below. To keep it up there you would have the arm extend past the pivot point into the bottom area and have this lower part of the arm attached to the opposite sides of a frame by springs to both sides.

Although not as effective and long lasting as a normal pendulum I wonder if this can be done to create an upside down pendulum that ticks for awhile...

Now, I then have the question, would this upside down pendulum tick faster when it is on a table in higher relative gravity or would it tick slower for higher relative gravity - opposite to its normal counterpart?

 

[Ich]

Now, I then have the question, would this upside down pendulum tick faster when it is on a table in higher relative gravity or would it tick slower for higher relative gravity - opposite to its normal counterpart?

it would tick slower. But I think this question should belong to general physics, there's nothing relativistic about it.

 

[gonegahgah]

Kool thanks ich.

 

[Dale]

The upside-down pendulum is unstable. If the springs were strong enough to stabilize it then, by definition they would dominate the behavior. You would essentially have a mass-spring system that would oscillate.

EDIT: actually, I just realized, a pendulum is only approximately a simple harmonic oscillator. The first (non-constant) term in the potential is quadratic, but there are also higher-order terms. If the springs exactly canceled out the quadratic term of the pendulum potential then you would be left with a stable fourth-order potential. It would oscillate, but not in simple harmonic motion. Also, it would not work right in different g fields. Higher fields and it would become unstable and lower fields and the spring would dominate.

 

[gonegahgah]

I thought that might be the case, thanks Dale. You could only use it for a short range of comparative gravities before you would have to change the springs to one suited for the new range. Still, I'm pleased I have been able to think up a pendulum system that - way less than perfectly - at least mimics (poorly) the way time is affected in under gravity in the same direction of increase; whereas a normal pendulum is the opposite..

That's all I was curious about. Though of course a falling pendulum won't tick at all which is unlike the way time 'ticks' even when in free fall.