Question:

How do sines and cosines relate to your RX-8 coilovers when parked?

(Nothing to do with dynamic spring rates. Talking basic math here.)

They provide a transcendental experience ;)

Viewed from the side the coils follow a sine wave.

I say they follow a cosine wave.
definitely cosine, 45 degrees out of phase it seems :p
http://www.leda.com/images2004/eibachracespring.jpg

when parked... id say the coilovers are acting more like a straight line; its not doing anything... but when you're on the road, the distance that the spring expands and contracts from its natural position can resemble the sin graph in a way...

Bingo! Sines and cosines are just two-dimensional projections of a three-dimensional helix - a spring. (Cosine being 90 degrees out of phase, actually.) I did a demo for some 4th graders a few weeks ago by stretching a Slinky on an overhead projector. It was neat to hear them gasp with a collective a-ha.

You can study trig and dynamics for years without anyone pointing out this basic geometric relationship between waves, circles and springs. (This is why you can define sine in terms of pi.) While it certainly applies to car design, the topic of discussion that day with those kids was music and guitars.

looks like it has a shorter period than 2pi

(Cosine being 90 degrees out of phase, actually.)
haha doh! I knoew I should have just written pi/2 :o

looks like it has a shorter period than 2piOk. The perspective in the coilover photo doesn't make for the most accurate graph. Seeing that you're from Princeton, I'll give this another try... Here's a precise plot of how these waves are just projections of a spring, with all three being generated by simply turning around a circle:

(This plot graphically shows how a cosine is 90degs out from a sine.)

ah ok, i see it now.

Bingo! Sines and cosines are just two-dimensional projections of a three-dimensional helix - a spring. (Cosine being 90 degrees out of phase, actually.) I did a demo for some 4th graders a few weeks ago by stretching a Slinky on an overhead projector. It was neat to hear them gasp with a collective a-ha.

You can study trig and dynamics for years without anyone pointing out this basic geometric relationship between waves, circles and springs. (This is why you can define sine in terms of pi.) While it certainly applies to car design, the topic of discussion that day with those kids was music and guitars.

But then pendulum associations don't fit into that theory do they?

Sines and cosines mesaure things that follow a cicrular theory, that is why they are mesured in radians typically, which is associated with pi.

Sines/cosine graphs measure movement, a still spring would graph as nothing, because it is not doing anything.

For further reading, you can try googling the "bit of string" hypothesis. Which basically says the smallest unit of matter are small bits of srting that oscillate in different resonance states from home state. It satisfies the fact that electrons cannot be particles.

"Dynamic srping rates" only have to do with compression studies, not anything at al with sine/cosine function. They could commonly be graphed using log functions and polynomials.

PS- to define something as out of phase, you need to first to define the home phase. (aka - inphase/outofphase lingo is only used when comparing 2 waves.)

Staticlag:
But then pendulum associations don't fit into that theory do they?

Sines and cosines mesaure things that follow a cicrular theory, that is why they are mesured in radians typically, which is associated with pi.

Pendulum oscillations can be very closely approximated by a pure sine wave. But the helix projection is exact. Mathematically perfect.
(Posted below is a two dimensional graph of a circle projected into a sine wave.)

Sines/cosine graphs measure movement, a still spring would graph as nothing, because it is not doing anything.

What was being graphed is the static geometry. The coilover waves can be shown with or without movement, kind of like the ocean. Take a picture, and you see waves. Take a video, and you still see the waves.

For further reading, you can try googling the "bit of string" hypothesis. Which basically says the smallest unit of matter are small bits of srting that oscillate in different resonance states from home state. It satisfies the fact that electrons cannot be particles.

What is most bizarre about string theory is when you probe the nature of the strings themselves. They are mathematical constructs. Pure imagination!

"Dynamic srping rates" only have to do with compression studies, not anything at al with sine/cosine function. They could commonly be graphed using log functions and polynomials.

If you remove the damping, the coilovers will oscillate in a sine wave at their natural frequency (the spring rate). The cliched scene of someone needing new shock absorbers (dampers) is when their car bobs up and down repeatedly.

PS- to define something as out of phase, you need to first to define the home phase. (aka - inphase/outofphase lingo is only used when comparing 2 waves.)

Two waves can coexist within the same object. In this case we are taking a spring and looking at it from two different directions and seeing two different waves. For those of us who remember record players, this is how they could get stereo signals out of one needle. The left and right channels existed in one groove. Since the waves were at a right angle to each other, movement of the needle in one channel produced no input on the other channel.

Here is the plotting of a cosine (90deg out of phase with the sine)...

It all comes from circles.

One more to complete the picture...