The displacement of a particle is given by $\vec{r} = A (\vec{i} \cos ω t + \vec{j} \sin ω t) .$ The motion of the particle is
(a) simple harmonic
(b) on a straight line
(c) on a circle
(d) with constant acceleration

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Solution

(c) on a circle

We know, $\frac{d^{2}}{d t^{2}} \vec{r} = - ω^{2} \vec{r}$
But there is a phase difference of 90^o between the x and y components because of which the particle executes a circular motion and hence, the projection of the particle on the diameter executes a simple harmonic motion.

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