so if a system is undergoing simple harmonic motion, you can model its frequency using pi and some intrinsic constants for that system
so for a spring, its root(k/m), divided by 2pi
for an LC system, its root (1/LC), divided by 2pi
but now suppose a human being is willfully moving his index finger between two points a and b in perfect simple harmonic motion
what intrinsic constants do you use to calculate the frequency?
the cool thing about this problem is that there's two planes
the first is based on his subjectivity, so you would say "need the constants pertaining to his contingent brain in order to predict what frequency he will decide to oscillate at, at any time t"
the second plane is a bit more interesting. its like "okay, suppose you both agree on a frequency, say 2 Hz per cycle. still, HOW could you calculate that frequency based on intrinsic constants about the human? surely his bone density, size (kind of the "mass"), muscular elastic coefficients, but you still need more...he is "telling" his muscle fibers how hard to push to achieve a given frequency, so neural signal potentials need to be incorporated as well
so you'd basically model this SHM as perfectly periodic neural pulses at a magnitude A and frequency f to opposing muscle fibers in order to move the finger at a given frequency between two points
but here's the problem: the frequency that you'd be pulsing those neurons would be the same as the index finger! you can't incorporate a "source frequency" term to solve for the frequency of SHM, that's circular, you need to model it in terms of intrinsic constants, divided by 2pi....
so for a spring, its root(k/m), divided by 2pi
for an LC system, its root (1/LC), divided by 2pi
but now suppose a human being is willfully moving his index finger between two points a and b in perfect simple harmonic motion
what intrinsic constants do you use to calculate the frequency?
the cool thing about this problem is that there's two planes
the first is based on his subjectivity, so you would say "need the constants pertaining to his contingent brain in order to predict what frequency he will decide to oscillate at, at any time t"
the second plane is a bit more interesting. its like "okay, suppose you both agree on a frequency, say 2 Hz per cycle. still, HOW could you calculate that frequency based on intrinsic constants about the human? surely his bone density, size (kind of the "mass"), muscular elastic coefficients, but you still need more...he is "telling" his muscle fibers how hard to push to achieve a given frequency, so neural signal potentials need to be incorporated as well
so you'd basically model this SHM as perfectly periodic neural pulses at a magnitude A and frequency f to opposing muscle fibers in order to move the finger at a given frequency between two points
but here's the problem: the frequency that you'd be pulsing those neurons would be the same as the index finger! you can't incorporate a "source frequency" term to solve for the frequency of SHM, that's circular, you need to model it in terms of intrinsic constants, divided by 2pi....
:D
also, a separate side-investigation should concern the origin of the pi term in the frequency of any oscillating system. its like, im just dangling a pendulum here, and suddenly pi is involved? any cyclical motion, any periodic recurrence (the pulsing of an LED)...that's all pi
