Question
Hard
Solving time: 5 mins
Q. 14. A point moves in the plane according to the law cos , where , and are positive constants. Find: (a) the trajectory equation of the point and the direction of its motion along this trajectory; (b) the acceleration of the point as a function of its radius vector relative to the origin of coordinates.
Text solutionVerified
(a) From the Eq :
(1)
And from the equation :
From Eqs (1) and (2), we get :
or,
which is the standard equation of the ellipse shown in the figure, we observe that,
at and
and at
and
Thus we observe that at t = 0, the point is at point 1 (Fig.) and at the following moments, the co-ordinate diminishes and becomes positive. Consequently the motion is clockwise.
(b) As x = d sin ωt and y=b cos ωt
So we may write
Thus
(1)
And from the equation :
From Eqs (1) and (2), we get :
or,
which is the standard equation of the ellipse shown in the figure, we observe that,
at and
and at
and
Thus we observe that at t = 0, the point is at point 1 (Fig.) and at the following moments, the co-ordinate diminishes and becomes positive. Consequently the motion is clockwise.
(b) As x = d sin ωt and y=b cos ωt
So we may write
Thus
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Question Text | Q. 14. A point moves in the plane according to the law cos , where , and are positive constants. Find:
(a) the trajectory equation of the point and the direction of its motion along this trajectory;
(b) the acceleration of the point as a function of its radius vector relative to the origin of coordinates. |
Topic | Oscillations |
Subject | Physics |
Class | Class 11 |
Answer Type | Text solution:1 |
Upvotes | 55 |