For each of the following parametric curves plot approximately its trace T (if y : R → R" , then the trace of y is the set of all y(t) e R", with te R. Assuming that the curve gives the motion of a particle, describe the motion in words. (a) y: R → R³, y(t) = (t², t, 2) (b) 9: R → R³, y(t) = (cos² t, sin² t) (c) b: R → R³, v(t) = (cos² t, sin t)
For each of the following parametric curves plot approximately its trace T (if y : R → R" , then the trace of y is the set of all y(t) e R", with te R. Assuming that the curve gives the motion of a particle, describe the motion in words. (a) y: R → R³, y(t) = (t², t, 2) (b) 9: R → R³, y(t) = (cos² t, sin² t) (c) b: R → R³, v(t) = (cos² t, sin t)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:For each of the following parametric curves plot approximately its trace T (if y: R → R", then
the trace of y is the set of all y(t) e R", with te R. Assuming that the curve gives the motion
of a particle, describe the motion in words.
(a) y: R → R³, y(t) = (t², t, 2)
(b) y: R → R³, p(t) = (cos² t, sin² t)
>
(c) : R → R³, v(t) = (cos² t, sint)
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