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Please please please help me?
To study the motion of the point determining the trajectory of velocity and acceleration if the law of motion of the point is in the figure below in which a, b, w are positive constants.
- Dr. ZorroLv 73 months agoFavorite Answer
The position vector r traces out an ellipse with semi-major axis a and semi-minor axis b. The parametric equation for r(t) is given. By differentiating r with respect to time you find the velocity vector. A second differentiation gives the acceleration vector.
r(t) = ( a cos(ω t) , b sin(ω t), 0 )
v(t) = ( - a ω sin(ω t), b ω cos(ω t), 0 )
a(t) = ( -a ω^2 cos(ω t), - b ω^2 sin(ω t), 0)
Note that a(t) = - ω^2 r(t)
The trajectories in v-space and a-space are ellipses too.
- ?Lv 73 months ago
What is your question? If "c(ωt)" is shorthand for "cos(ωt)" and "s(ωt)" is shorthand for "sin(ωt)," then the velocity is
| -a·ω·s(ω·t) |
| b·ω·c(ω·t) .|
|........ 0 .......|