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mcc

Maximum speed of a balance wheel...

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Hi,

this is just a question out of couriosity... :)

My SEIKO SNK809 has a 7S26C movement. Its balance wheel has roughly a 4.5mm radius (I measured that with a transparent ruler on the transparent
back of the watch...if someone has the exact value I would be the last one, who insists of the value mentioned above....;) ). From that I can calculate the circumference
of the balance wheel. Assuming an amplitude of 260 degree gives me the way a point travels on the balance wheel by multiplying the circumference by 26/36.
Furthermore this way is traveled 21600 times an hour. This gives me the linear speed of that point.
BUT: The speed changes in accordance to a sine function...
And here I got stuck: speed is the derivation of distance by time. The derivation of sine(t) dt gives me a cosine function...and I am again right from where I started..with a 90 degree phase shift.
How can I calculate the maximum speed of a point traveling in accordance to a sine function around a circumference if I know the speed it would need to have, when it would be linear motion? I cannot get my head around it... ;)

HEEEEEELLLLLPPPPP!  :):):)

Cheers!
mcc

 

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Equation of motion is sinesoidal , so it's velocity is derivative of sine function which is cosine function , parameters giving maximaum speed  times it's cosine function gives you istantaneous speed.

S=s max × cos(alpha)     

S max is the speed you explained calculation of. S max occures at alpha=0.

S= 2πr( 26/36) ( frequency) × cos( alpha) 

 

 

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Both velocity and speed vary sinusoidally.  

The fact that velocity is a vector and speed scalar quantity, shouldn,t cause  doubts in your mind that speed is unworthy of following a sinusoidal behaviour, is this where you let doubts get in your visualising the system?

Your understanding of the rest is good, I don,t see what caused your doubts.

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Hi Nucejoe,

My problem was the step from the (hypothetical, in this physically not existing) linear speed to the way to find the maximum. Until you post the solution  :)

Thanks a lot for that!!!   :)

Cheers!
mcc

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