Determining cycles

[sajib_mostofa]

When you are given a position vector and the question asks you how long it takes to complete one cycle or something along those lines, whats the easiest way to do it?

[JinXi]

How I do it is For example r = sin(t) i  +  3cos(t) j

Let t= 0  and find the point where it starts,

for this (0,3)

then, solve i and j components for i=0 and j = 3
which gives me t= n(pi) for i, and t= 2n(pi) for j. where n are All Natural Numbers.

from this I can see that one cycle takes 2pi to complete.
  

Edit: Lowest Common Factor of 2 Periods should work aswell.

[will74]

Find initial position, r(0) then solve for i and j components = r(0) to get t, that's how long it takes to get back to starting position. Make sure the t value gives the r(0) vector for both i and j components (and k potentially). Depending on the context of the question it may be more than this t value, e.g. On one past vcaa paper they had a toy train which passed through the origin twice in a full circuit

[sajib_mostofa]

Cheers for that guys