Question

A point moves in the plane xy according to the law x = a sinωt, y = b cosωt, where a, b, and ω are positive constants. Find:

(a) the trajectory equation y (x) of the point and the direction of its motion along this trajectory;

(b) the acceleration w of the point as a function of its radius vector r relative to the origin of coordinates.

Answer 1

(a) From the eqn : x = asinωt

which is the standard equation of the ellipse shown in the figure.

we observe that,

Thus we observe that at t = 0, the point is at point 1(fig.) and at the following moments, the co-ordinate y diminishes and x becomes positive.consequently the motion is clock-wise.