Need a Boffin ...

[Bluechip]

Hi Troops

Assume I have a circular eccentric with a follower.

The Displacement of the follower is Simple Harmonic Motion ie. a SINE curve.  [ YES/NO ] ??

So, is the Acceleration  of the follower a COSINE ????    [ YES?NO ] ??

It looks like it, but no way can I find anywhere on the net that tells me in simple language.

Used to have a book titled Wave Physics, can't find that either ...   

If it is not Cosine, what is it ??

Dave BC

 

[Dan Rowe]

Dave,
Yes it is simple harmonic motion. It is the same as a piston and a crank, the eccentric throw is the crank arm.

Here is the best explanation of the formulas I could find:
http://en.wikipedia.org/wiki/Piston_motion_equations

Dan

[swilliams]

If the displacement is a sin wave

the speed will be a cos()

the acceleration will be sin() again. It is in the opposite direction of the displacement. If you multiply the displacement by the angular frequency squared you get the acceleration.

In your case the angular frequency will be given by rotations per second multiplied by 2 x pie
pie = 3.14.....

Steve

[zeeprogrammer]

Had to look up 'Boffin'...

From the UrbanDictionary:
   
"Colloquial word used to refer to highly trained specialists in their respective fields; especially when the exact field of specialty is unknown.
Usually used when an new and unknown piece of technology is being discussed, and having no idea what branch of speacialty is responsible."

Can also be used as an insult. Not in this case! But I have some use for it tomorrow at work. 

[tvoght]

I'll go with Boffin Steve on this one.

cosine is the derivative (rate of change) of sine.
sine is the derivative (rate of change) of cosine.

Velocity is the rate of change of position.
Acceleration is the rate of change of velocity.

So the velocity of the sinusoidal motion of the follower is cosine.
The acceleration of the follower motion is in phase with the position (sine again).

Some thought experimentation:

When the follower is at the end of its travel, its velocity is passing
through zero. Its acceleration is at a maximum (its reversing direction!).

When the follower is at mid-stroke, its velocity is at a maximum while it's
acceleration is passing through zero. This tells us that at near mid-stroke,
the velocity is nearly constant.


--Tim

[steamer]

If the displacement is a sin wave

the speed will be a cos()

the acceleration will be sin() again. It is in the opposite direction of the displacement. If you multiply the displacement by the angular frequency squared you get the acceleration.

In your case the angular frequency will be given by rotations per second multiplied by 2 x pie
pie = 3.14.....

Steve

Acceleration (time rate of change of velocity) should be -sin().....IIRC.... ......which I think is correct anyway...dv/dt.

Actually Steve...you said opposite direction......

Dave

[Bluechip]

Thanks for the info. Lot there to think about. Long time since I did differential calculus ... 

I suspected cosine was too simple to be true .... 

Couldn't prove it . All I could find on the www were spring/mass systems a pendulums, neither of which seemed relevant.

Found my book now .. good job, a new one is ?260 it seems 

http://www.amazon.co.uk/s/ref=nb_sb_ss_i_0_7?url=search-alias%3Daps&field-keywords=wave+physics&sprefix=wave+ph%2Caps%2C203

Used one a bit cheaper at a fiver ... 

Dave BC

[mklotz]

Just to clarify...

position = sin(w*t)

where:

w = angular rate (rad/sec)
t = time

velocity = time derivative of position = w * cos(w*t)

acceleration = time derivative of velocity = - w^2 * sin(w*t)

Each of these quantities is a vector so that minus sign in the acceleration matters because it says the acceleration points the opposite direction of the position.

Oh, and 3.14159... is termed "pi", one of the letters of the Greek alphabet.  "Pie" is something one eats with a tankard of ale or, in the States, a popular dessert, often fruit-filled.

[IanR]

Just to clarify...




  "Pie" is something one eats with a tankard of ale or, in the States, a popular desert, often fruit-filled.

I thought that in the US a popular desert would be Nevada.

[mklotz]

Indeed!  I'll fix that right away.

[NickG]

 

[steamer]

Please note my high degree of restraint Marv!...I want brownie points for this!

Dave

[mklotz]

Damn, one brain fart and the vultures are on you.  Ok, you and Nick get a freebie.  Your freebie was used up when I didn't comment on your recent extremely creative spelling of innocuous using a 'q'.

[tel]

Soooooooo ...... they don't eat pie in Nevada then?

[tvoght]

I'm reminded of the hoosier who had just  been told how to determine the area of a circle:

"No! No! Pie r round. Cornbread r square!"

--Tim