Question

A particle is subjected to two simple harmonic motions along $x$ and $y$ directions according to $x=3\sin 100\pi t$ $y=4\sin 100\pi t$

• A. Motion of particle will be on ellipse travelling in clockwise direction.
• B. Motion of particle will be on a straight line with slope $\frac{4}{3}$
• C. Motion will be simple harmonic motion with amplitude $5$.
• D. Phase difference between two motions is $\frac{\pi }{2}$.

Answer 1

The correct option is A Motion of particle will be on ellipse travelling in clockwise direction.

$x=3\sin 100\pi t$

$y=4\sin 100\pi t$

Equation of path is $\frac{y}{x}=\frac{4}{3}$

ie,. $t=\frac{4}{3}x$

which is equation of a straight line having slope $4/3$.

Equation of resulting motion is

$\overrightarrow{r}=x\hat{i}+y\hat{j}=(3\hat{i}+4\hat{j})\sin 100\pi t$

Amplitude is $\sqrt{3^2+4^2}=5$