Post by: squance on April 05, 2008, 02:49:15 pm
For the following function describing a particle's position at time t, find the equation fo tthe path and state the period of the motion of the path.
u = 2cos(2t)i + 2sin(2t)j
well for the first part I got...
u = 2cos(2t)i + 2sin(2t)j
x(t) = 2cos(2t) y(t) =2 sin (2t)
x^2 = 2^2 cos^2(2t) y^2 = 2^2 sin^2(2t)
x^2 + y^2 = 4 cos^2(2t) + sin^2(2t) = 1
x^2 + y^2 = 4 (equation of circle with center at (0,0) and radius 2)??
Then for the period of the motion...we choose two values of t and sub them into u, right??
when t = 0...
u = 2cos(0)i + 2 sin(o)j
i + 2j
=(0,2)
when t = 2
u = 2 cos (2X2)i + 2cos(2x2)j......
u = 2 cos4 i + 2 cos (4) j....
(I don't know how to work out the above line...)
Can someone hlep. me plese?? I think the period of the motion is pi or something but I don';tknow how...
Post by: Mao on April 05, 2008, 03:00:59 pm
The process to derive the period of motion is easier than you think.
looking at
the period of the circular functions here are
hence the period of u is
Post by: squance on April 05, 2008, 03:08:06 pm
Post by: Mao on April 05, 2008, 03:10:31 pm
what do u mean by "direction"??
when you sub t into u you would get a position vector..
Post by: squance on April 05, 2008, 03:14:48 pm