# Sinusoidal force mechanism for a swing

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## Summary:

I'm just curious to know that how a sinusoidal 'push' could be used for a swing. I was trying to solve another problem but I believe knowing this could help me to solve the other problem.
Hi,

Please have a look on the attachment. The displacement of swing from the equilibrium position, x=0, is considered to be maximum, +x, when the swing reaches the person who is pushing it. The pushing force is of short duration and could be approximated by a pulse. I hope I have it correct.

How can sinusoidal force be applied instead of pulses? I think it would require some kind of a motorized mechanism but I can't imagine it would work or implemented. Could you please help me with it?

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A.T.
I think it would require some kind of a motorized mechanism but I can't imagine it would work or implemented.
Sounds like an engineering project. Do you have specific questions about the physics?

Dale
Mentor
Summary:: I'm just curious to know that how a sinusoidal 'push' could be used for a swing. I was trying to solve another problem but I believe knowing this could help me to solve the other problem.

How can sinusoidal force be applied instead of pulses?
Use a spring.

anorlunda and Lnewqban
In an exaggeration, imagine that your pulse hits the sinusoidal curve only at ##\pi/4## and ##3\pi/4##.
It seems that a pulse would act more as two successive impacts (and perhaps as a resistive brake in between) than a modulating push.

A sinusoidal movement is a projection of a rotating mechanism:

http://507movements.com/mm_090.html

Last edited:
Sounds like an engineering project. Do you have specific questions about the physics?
No, I can assure you that it's not. If it were, I would have told you.

Use a spring.
I had thought about it but wouldn't it require two springs? Most importantly, I cannot picture how the push would be incorporated into the spring system so that with each push the swing goes higher.

I'm sure they use such a mechanism for the swings in amusement park. How can a rotational motion of a motor be changed into sinusoidal force? I don't even know the exact wording so that I could Google it.

In an exaggeration, imagine that your pulse hits the sinusoidal curve only at π/4π/4\pi/4 and 3π/43π/43\pi/4.
It seems that a pulse would act more as two successive impacts (and perhaps as a resistive brake in between) than a modulating push.
Yes, the timing is important. You need to sync your pushes with the swing frequency otherwise your pushes would act like brakes.

In the picture from my first post, the push is applied at 90 degrees of the swing's motion.

But the issue is to be at the correct frequency exactly or the phase between driver and driven will slowly go bad. There is a wonderful electronic circuit called a phase-locked-loop which I leave on the table.
Anything you do will require frequency feedback somehow.

Dale
Mentor
Most importantly, I cannot picture how the push would be incorporated into the spring system so that with each push the swing goes higher.
So then maybe you don’t actually want a sinusoidal push.

Any push you give will have the same problem......you need it to phase lock. (Or the timing has to be demanded by the swing.....which is the same thing really).
Whenever I am in my hammock, I attempt to devise a simple system.......there seems to be no such animal (at least within my usually fertile imagination for mechanical contrivance) . Ideas??

jbriggs444
Homework Helper
2019 Award
Any push you give will have the same problem......you need it to phase lock. (Or the timing has to be demanded by the swing.....which is the same thing really).
Whenever I am in my hammock, I attempt to devise a simple system.......there seems to be no such animal (at least within my usually fertile imagination for mechanical contrivance) . Ideas??
If you solve the equations, you will find that timing of the solution is a function of the driver, not of the [idealized] swing.

Amplitude is a function of how well the two are matched.

https://en.wikipedia.org/wiki/Harmonic_oscillator#Sinusoidal_driving_force

etotheipi and PainterGuy
Yes. And this is a very high Q oscillator. So next time you are pushing a child in a swing, you choose the frequency and see how well that works out.....

etotheipi, anorlunda, Dale and 1 other person
The simplest ideas I have had seem to involve a clutch or dashpot the produces more coupling force at low relative speed than high, but I don't know how to do that easily. This would allow an otherwise uncontrolled motor to push more with the swing than against and so increase amplitude.......I need some negative viscosity fluid! Simple is the operative word here.

That would be one way to do it. I would prefer something a little less finicky if possible and better suited to the hammock geometry. My best (hypothetical) solution so far is in fact an optically triggered magnetic puller (like often used on Foucalt Pendulum setups).
I was hoping to make something like Tacoma Narrows vortex shedding that would be drop dead simple and self-regulating.
I mean I don't really need a motorized hammock unless its really clever.

So then maybe you don’t actually want a sinusoidal push.
I do want to understand a general system which could do that. I don't want exact details because I'm not going to implement it. In the past I was also trying to understand how a mechanical motorized system could be built which could provide a pendulum like motion. The swing motion is also similar.

The problem could be phrased as follows. How to convert circular/motor motion into simple harmonic motion?
Thank you.

https://en.wikipedia.org/wiki/Reciprocating_motion

jbriggs444
Homework Helper
2019 Award
I do want to understand a general system which could do that. I don't want exact details because I'm not going to implement it. In the past I was also trying to understand how a mechanical motorized system could be built which could provide a pendulum like motion. The swing motion is also similar.

The problem could be phrased as follows. How to convert circular/motor motion into simple harmonic motion?
Thank you.

https://en.wikipedia.org/wiki/Reciprocating_motion
It can be harder to solve a toy problem than a real problem. Details matter. Details that are missing from toy problems. How perfect does the motion need to be? What kind of load must be driven? How long does it need to last? How big must the motion be? How efficient does it need to be?

We could use a worm gear drive to push a cam follower through any smooth motion pattern you like.

PainterGuy, Dale and Lnewqban
Dale
Mentor
How to convert circular/motor motion into simple harmonic motion?
That is pretty straightforward. If you have a T shaped bar where the top of the T has a slot where the motor arm can move left and right freely and the "trunk" of the T can slide up and down then you will convert circular motion into vertical simple harmonic motion.

PainterGuy, hutchphd, Lnewqban and 1 other person
anorlunda
Staff Emeritus
The problem could be phrased as follows. How to convert circular/motor motion into simple harmonic motion?
People have been doing that for roughly 1000 years. Here are 2 examples.

PainterGuy
etotheipi
Gold Member
2019 Award
The problem could be phrased as follows. How to convert circular/motor motion into simple harmonic motion?
Also similar to things like crank mechanisms for train wheels. This example is not harmonic motion (i.e. try writing the position of the slider/piston as a function of the angle of the radial arm, which goes as ##\theta = \omega t##), though approaches SHM if the length of the long arm gets really big compared to the radial arm.

PainterGuy and Lnewqban
jrmichler
Mentor
How can sinusoidal force be applied instead of pulses?
Here's an idea. A crankshaft with connecting rod connected to the swing high up near the pivot. The connecting rod pushes on the swing rope and exerts a force on the swing when the rope deflects. If the drive frequency approaches the swing natural frequency, the force will approach zero. If the drive frequency is near the swing natural frequency, the result will be a beat frequency, where the swing amplitude, at the swing natural frequency, will continuously change from near zero to a maximum and back to near zero. If the drive frequency is very low, much less than the swing natural frequency, the kid will barely move. If the drive frequency is very high, much higher than the swing natural frequency, the kid will perceive that (s)he is sitting on a vibrator. The crank radius and the attach point will determine the maximum swing amplitude.

The connection needs to be up near the pivot. If the connecting rod was attached to the swing seat, and the frequency set too high, the kid would get flung out.

This is not a true force input. A true force input would drive a simple spring mass system amplitude toward infinity at the natural frequency. But then, a swing is not a simple spring mass system and the natural frequency changes at large amplitudes.

PainterGuy
It can be harder to solve a toy problem than a real problem. Details matter. Details that are missing from toy problems. How perfect does the motion need to be? What kind of load must be driven? How long does it need to last? How big must the motion be? How efficient does it need to be?
Thank you. In general, I do agree with you but if I knew the details that well, I'd say that I wouldn't have asked this question!

That is pretty straightforward. If you have a T shaped bar where the top of the T has a slot where the motor arm can move left and right freely and the "trunk" of the T can slide up and down then you will convert circular motion into vertical simple harmonic motion.
Thank you.

"If you have a T shaped bar where the top of the T has a slot where the motor arm can move left and right freely" - I think motor arm can move left and right only if motor's rotational motion is translated into reciprocating motion of some piston-like device which moves left and right as a result of motor rotational motion.

"and the "trunk" of the T can slide up and down then you will convert circular motion into vertical simple harmonic motion." - I'm sorry but I couldn't understand it. My apologies if I'm picturing it totally wrongly.

People have been doing that for roughly 1000 years.
Thank you for letting me know that my thinking level is 1000 years behind...

Also similar to things like crank mechanisms for train wheels. This example is not harmonic motion (i.e. try writing the position of the slider/piston as a function of the angle of the radial arm, which goes as ##\theta = \omega t##), though approaches SHM if the length of the long arm gets really big compared to the radial arm.
Thank you. I think if the connection at "B" between arms "2" and "3" was permanent then the motion of slider/piston, labelled "4", would become SHM. Please correct me if I'm wrong.

Source: https://www.britannica.com/technology/slider-crank-mechanism

Here's an idea. A crankshaft with connecting rod connected to the swing high up near the pivot. The connecting rod pushes on the swing rope and exerts a force on the swing when the rope deflects. If the drive frequency approaches the swing natural frequency, the force will approach zero. If the drive frequency is near the swing natural frequency, the result will be a beat frequency, where the swing amplitude, at the swing natural frequency, will continuously change from near zero to a maximum and back to near zero. If the drive frequency is very low, much less than the swing natural frequency, the kid will barely move. If the drive frequency is very high, much higher than the swing natural frequency, the kid will perceive that (s)he is sitting on a vibrator. The crank radius and the attach point will determine the maximum swing amplitude.

View attachment 261144

The connection needs to be up near the pivot. If the connecting rod was attached to the swing seat, and the frequency set too high, the kid would get flung out.

This is not a true force input. A true force input would drive a simple spring mass system amplitude toward infinity at the natural frequency. But then, a swing is not a simple spring mass system and the natural frequency changes at large amplitudes.
Thank you.

Possibly, one can use stiff rods in place of a rope.

"If the drive frequency is very low, much less than the swing natural frequency, the kid will barely move. " - If rods are used instead of rope then the swing seat would move very, very slowly.

"The crank radius and the attach point will determine the maximum swing amplitude." - Attach point "B" would play an important role where "A" is pivot point. Think of torque=(force)*(distance_from_pivot_point).

If the crank radius is too small then attach point "B" would move around a short distance from its equilibrium position.

"A true force input would drive a simple spring mass system amplitude toward infinity at the natural frequency." - Yes, a theoretical mass spring system where spring could be extended to infinity and compressed to negative infinity around its equilibrium position.

But there is a problem. The force won't be purely sinusoidal. Wouldn't it more of 'reciprocating' force?

Note to self:
/watch?v=Ca91iOVGd9A (beat frequency, insert "youtube.com" in the front)

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Dale
Mentor
I think motor arm can move left and right only if motor's rotational motion is translated into reciprocating motion of some piston-like device which moves left and right as a result of motor rotational motion
I have no idea why you would think that. It is not correct. The motor arm moves in a circle which is a left and right motion combined with an up and down motion. The T allows the arm to move left and right freely and only the up and down part of the motion pushes the T up and down.

Edit: apparently it is called a Scotch yoke. Here is a diagram oriented sideways from my description and with an extra “trunk” piece.

https://en.m.wikipedia.org/wiki/Scotch_yoke

PainterGuy