Frictionless Swing: Exploring Natural Frequency with a Rider

[Loren Booda]

A frictionless system consists of a swing of given length and its massive rider, initially at rest. Is it possible for the rider to kick this system into its unforced natural frequency?

 

[russ_watters]

If by swing you mean pendulum (or spring or any similar system), then yes. Such a system can only oscillate at its natural frequency unless it is under constant driving force.

 

[Loren Booda]

But can that frictionless pendulum's (approximately) harmonic motion be initiated from rest by a kicking force within the bob? Does such a system have the opportunity to move other than by that driving force?

 

[HallsofIvy]

"within" the bob? Are you thinking of a person sitting on a swing, motionless, attempting to start the swing in motion without any outside force?

If you allow friction: air resistance, friction of the "chain" on the support (i.e. some way to bring outside forces into play), then yes, it is possible.

Without friction, so that all forces are internal, then "conservation of momentum" says that we cannot change the momentum of the system by inside forces.

 

[Loren Booda]

Thanks, Halls, that's what I suspected.

 

[krab]

Originally posted by HallsofIvy
Without friction, so that all forces are internal, then "conservation of momentum" says that we cannot change the momentum of the system by inside forces.

Umm.

Momentum isn't conserved. Think of a freely swinging pendulum. Momentum varies sinusoidally. Momentum is only conserved when the potential is independent of the coordinate conjugate to the momentum.

Can the pendulum start swinging from motions inside the bob? Think of the following situation. The bob consists of 2 massive halves under tension from a spring, but held together with a string. The string suddenly breaks and the 2 halves spring apart. The centre of mass of the system doesn't move initially, but imagine that the string is attached to one of the 2 halves. The string, being massive, is suddenly at a finite angle with respect to vertical. We now have a compound pendulum, which definitely is not in an equilibrium state. The two halves will start to swing about the attachment point, and the centre of mass will move.

 

[russ_watters]

Originally posted by krab
We now have a compound pendulum...

Ie, a kid sitting on a swing.

 

[Loren Booda]

My question again: for a frictionless pendulum initially at rest, can any movement "within" the bob, now having ceased, have caused the pendulum to continue at its nonzero natural frequency? This holds for a compound or a simple pendulum.

 

[russ_watters]

Originally posted by Loren Booda
My question again: for a frictionless pendulum initially at rest, can any movement "within" the bob, now having ceased, have caused the pendulum to continue at its nonzero natural frequency? This holds for a compound or a simple pendulum.

That really doesn't make a lot of sense. It sounds like you are saying the starting conditions are no internal or external motion or forces. It will just sit there then. Newton's first law.

One confusing part is the word "continue." It can't "continue" moving if the starting conditions are of no motion.

And movement "now having ceased" in something initially at rest? Huh?

Maybe if you could reword it or describe the specific situation...

 

[Loren Booda]

Sorry, russ, my hurried wording. Perhaps:

Given a frictionless pendulum at rest. Its bob holds a mechanism which produces arbitrary kicks. Is it possible for the pendulum to attain its natural, nonzero harmonic motion when the mechanism stops kicking?

(You may have already answered this.)

 

[schwarzchildradius]

Definitely can, and it would swing back and forth 'forever' until gravitational energy slowed it down.
When you kick your legs out on a swing, you're changing the momentum of the entire swing-set. Change in momentum by definition causes a force, because momentum is a conserved quantity. Some antique clocks used a hidden swinging weight to cause a pendulum to move 'mysteriously.' Frictionless pendulums do not exist, but if modeled mathematically will exhibit the same basically undamped harmonic oscillation as orbiting bodies.

 

[russ_watters]

Originally posted by Loren Booda
(You may have already answered this.)

Yes, and the answer is yes. A pendulum not under continuous force can swing at only one frequency: its natural frequency.

 

[Doc]

I can't believe this thread made if this far before someone actually said "YES". Doesn't ANYONE here remember swinging as a kid? I as well as many other kids could manipulate the swing from a dead stop to full swing without their feet touching the ground. Was everyone here too busy with there nose in a book in the library to have time to actually have fun and be a kid? I don't personally know any of you but this thread would be a perfect example of a group of stereotypical egg-heads. Maybe everyone just mis-understood the question. I hope so.

 

[Loren Booda]

Doc

I as well as many other kids could manipulate the swing from a dead stop to full swing without their feet touching the ground.

Now try the same without friction - that was my contention.

 

[russ_watters]

Originally posted by Loren Booda
Doc Now try the same without friction - that was my contention.

Where is this friction you are talking about? Wind resistance? Its not enough to get you moving.

 

[Integral]

I understand the mechanism of getting a swing going from a stop is a change in center of mass, the rider rocks back and forth translating the CM of the swing system, this movement of the CM must match the natural frequency of the swing. Riders learn to feel the motion and modify the rhythm to maximize motion.

Friction is required to keep the rider in the seat.

 

[Njorl]

The way you start a real swing (with friction) is to displace your center of mass so that the system must rotate to reach minimum potential energy. You then shift your weight back before the system catches up with you. The reason you can do this is because the friction at the axis (top of the swing's rope) prevents instantaneous correction to the angle of the rope. You If there is no friction, you will not be able to displace your center of mass more quickly than the swing reacts.

Essentially, with no friction, you lean back and swing forward a tiny bit. As soon as you are done leaning, you stop swinging. You straighten up, and you swing right back to the original position the moment you are upright again. You never really "swing", you just wobble a bit. You never acquire any angular momentum.

Njorl

 

[Doc]

I would think that it is the momentum of the swing that prevents the swing from instantaneously reacting to the riders motion. I think it has little to do with friction.

 

[Loren Booda]

Njorl,

My guess (and what you seem to say) is that the bob can swing on an axis of its own, but not translate that motion to the frictionless swing.

 

[krab]

I suspect Njorl is right, but I'm bothered by the fact that I don't recall well-built, low-friction swings being any harder to start than crappy ones with lots of friction.

Here's something to try: Go to www.sodaplay.com[/URL], and construct a swing, with muscles in the right places. Hours of fun. I couldn't get one swinging at the swing's frequency; only at the muscle's frequency.

 

[Loren Booda]

krab,

"This page cannot be displayed."

 

[krab]

Sorry. I fixed it. There was an extra comma in it. Also, you have to have Java enabled.

 

[Loren Booda]

I've seen something like it on cable TV where the the machines evolve. Very pleasing to the eye and visceral.

I couldn't get one swinging at the swing's frequency; only at the muscle's frequency.

Whereso on the SODA website?

 

[krab]

Originally posted by Loren Booda
I've seen something like it on cable TV where the the machines evolve. Very pleasing to the eye and visceral. Whereso on the SODA website?

You construct one using sodaconstructor. First Clearall, Then select Fixed mass, and place the pivot point of the pendulum. Now select Free mass and place it somewhere below. Now click Simulate instead of Construct, and the swing begins to swing. You'll have to set k very large. It is the spring constant between the pivot and the seat; there are no rigid connections. And set the damping to zero for frictionless swing. Now comes the fun part. Elaborate the lower mass with connections and muscles to be some facsimile of a person pumping.

 

[russ_watters]

Ok, I think I have this figured out - we're looking at the problem backwards (or rather, from the side). The key here is the motion parallel to the string, not perpendicular. Ever stand up on a swing? Its harder to conceptualize with a swing when you are sitting down, but it works just like a yoyo - or better yet, a weight on a rubber band. If you bounce it in phase with its natural frequency, it doesn't continue after you stop. Out of phase (halfway?) and it does continue. Repeated out of phase driving will increase the oscillation. I'll need to work on this a little to see if I can figure out the math (gawd, I hate math). Or let me check out that program...

 

[Integral]

From simple energy considerations, it is not clear that friction has anything to do with the motion resulting from a change in CM (Center of Mass). As a pendulum swings the bob is continually changing in height, this is reflected in a change in Potential energy, this of course results in a change in kinetic energy.

When a rider pumps a swing, s/he is mimicing this change in potential energy by raising and lowring the CM of the swing system. The change in PE MUST be reflected in a change in KE. Thus the simple act of rocking back and forth is sufficient to set a swing into motion. As long as the frequency of the CM change is harmonic with the natural frequency of the swing motion will occur. The only need for friction is to keep your hands and bottom on the swing.

When standing you raise the CM considerably, thus reducing the natural frequency, further, when standing your mass is not concentrated, thus you need to do the analysis as a physical pendulumn with a distributed mass. Things change.

 

[Loren Booda]

Integral,

When a rider pumps a swing, s/he is mimicing this change in potential energy by raising and lowring the CM of the swing system. The change in PE MUST be reflected in a change in KE. Thus the simple act of rocking back and forth is sufficient to set a swing into motion. As long as the frequency of the CM change is harmonic with the natural frequency of the swing motion will occur.

However, can the (frictionless) swing remain in harmonic motion once the bob's rocking (started from a dead hang) has stopped?

 

[Integral]

Originally posted by Loren Booda
Integral, However, can the (frictionless) swing remain in harmonic motion once the bob's rocking (started from a dead hang) has stopped?

Looks to me like once the motion begins, it is simply a pendulumn. If no further pumping occurs, and there is no friction at the piviot, motion will continue indefinatly. The conversion between kinetic and potential energy will continue without loss.

 

[Njorl]

If there is no friction in the axis (where the swing contacts the support), won't the center-of-mass always be directly below the axis? You can cause some angular displacement of the rope but not the CoM.

However, can the (frictionless) swing remain in harmonic motion once the bob's rocking (started from a dead hang) has stopped?

Since there is no true swinging, when the oscillation stops, the swing remains motionless, with the CoM directly below the axis.

Njorl

 

[Jimbone]

This question is interesting but I think its as simple as pushing and pulling yourself around on a fixed object in space. Of course you can move because you have a fixed object to push and pull against, regardless of friction, air resistance etc.