Frictionless swing

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

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

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

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

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

russ_watters

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 aquire any angular momentum.

Njorl