Question

A particle is subjected to two simple harmonic motions along x and y directions according to $x=3\sin 100\mathrm{\pi t}$ and$y=4\sin 100\mathrm{\pi t}$. Choose the correct statement(s).

• 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

Answer: (B), (C)

The correct options are
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.

$x=3sin100\pi t$
$y=4sin100\pi t$
Equation of path is $\frac{y}{x}=\frac{4}{3}$
i.e., $y=\frac{4}{3}x$
which is equation of a straight line having slope $\frac{4}{3}$. Equation of resulting motion is
$\overrightarrow{r}=x\hat{i}+y\hat{j}=(3\hat{i}+4\hat{j})sin100\pi t$
Amplitude$=\sqrt{3^2+4^2}=5$

Phase difference between $x$ and $y$ motions is clearly zero.