question_answer 30)

                  A particle is acted simultaneously by mutually perpendicular simple hormonic motion \[x=a\,\cos \omega t\] and \[y=a\sin \,\omega t\]. The trajectory, of motion of die particle will be                 (a) an ellipse                      (b) a parabola                 (c) a circle                            (d) a straight line

Answer:

                  (c) \[\frac{x}{a}\,=\,\cos \,\,\omega \,t\] and \[\frac{y}{a}=\,\sin \,\omega t\]                 \[\therefore \] \[\frac{{{x}^{2}}}{{{a}^{2}}}\,+\frac{{{y}^{2}}}{{{a}^{2}}}\,\,=\,1\] or \[{{x}^{2}}\,+\,{{y}^{2}}={{a}^{2}}\]