Hi.

can u tell me how to calculate pitch (i mean the vertical distance between two revolutions)of a helix with parametric equatios [2cost 2sint 6t]..?

 

What you wrote does not look like a parametric equation. I would expect something like:

z = f(t)  ; z is some function of the parameter t
 
or
 
z = f(s,t) ; z is some function of parameters s, and t

what you wrote using square brackets looked like

[2cost 2sin6t]

if that is a row vector then it only represents a figure in 2-dimensions and so the concet of "height" is meaningless in that context.

 

i mean that there are three parameters

x=2cost

y=2sint
z=6t

(helix is increasing along z axis)

 

i mean that there are three parameters

x=2cost

y=2sint
z=6t

(helix is increasing along z axis)

OK, I see it now, it was a vector belonging to R3. I saw "sin 6t", instead of "sint 6t"

If you start at t=0, z=0 and goto t=2*pi, then z=12*pi

Does that make sense?

 

ok, i understand,we start from t=0,but how did u chose t=2*pi,(like i know that the circle completes its one revolution from 0-2*pi)but can you check that for this particular equation of helix
[ tsin2t tcos2t t^2 ]
will t still be fom 0 to 2*pi or will it be till pi only?

 

You are correct. With the parametric functions for x and y running at twice the frequency of the first example, one revolution in the xy plane will occur at t = pi

 

This is a really interesting exercise when applied to things like helical antennas. Only in recent years have they had the formulas down for optimum pitch/gain of a helical antenna....and it was done with brute force numerical methods. The helix is deceptively simple (or complicated, depending on your point of vew!) Optimizing a pitch becomes very complicated very fast when working with electromagnetics!

Eric