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Question
A particle moves in the X-Y plane according to the equation \[\overrightarrow{r} = \left( \overrightarrow{i} + 2 \overrightarrow{j} \right)A\cos\omega t .\]
The motion of the particle is
(a) on a straight line
(b) on an ellipse
(c) periodic
(d) simple harmonic
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Solution
(a) on a straight line
(c) periodic
(d) simple harmonic
The given equation is a solution to the equation of simple harmonic motion. The amplitude is \[( \overrightarrow i + 2 \overrightarrow j)A\] , following equation of straight line y = mx + c. Also, a simple harmonic motion is periodic.
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