The two-dimensional motion of a particle, described by $\vec{\mathrm{r}}=(\overset{^}{i}+2\overset{^}{j})\mathrm{Acos}\omega t$ is a/an:
A. parabolic path
B. elliptical path
C. periodic motion
D. simple harmonic motion

Choose the correct answer from the options given below :

Question

The two-dimensional motion of a particle, described by $\vec{\mathrm{r}}=(\overset{^}{i}+2\overset{^}{j})\mathrm{Acos}\omega t$ is a/an:
A. parabolic path
B. elliptical path
C. periodic motion
D. simple harmonic motion

Choose the correct answer from the options given below :

YESPYQ · Accepted Answer

Correct answer: d) C and D only. $\vec{r}=(\overset{^}{i}+2\overset{^}{j})A\cos \omega t$ $x=A\cos \omega t$ $y=2A\cos \omega t$ y = 2 x The path is straight line. The motion is SHM and periodic as $\frac{dr}{dt}=−\left(\overset{^}{i}+2\overset{^}{j}\right)\omega A\sin \omega t$ $\frac{{d}^{2}r}{d{t}^{2}}=−(\overset{^}{i}+2\overset{^}{j}){\omega }^{2}A\cos \omega t$ $\vec{a}=−{\omega }^{2}\vec{r}$

The two-dimensional motion of a particle, described by \(\vec{\mathrm{r}}=(\overset{^}{i}+2\overset{^}{j})\mathrm{Acos}\…

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