Oscillations Ques 16
16. Two simple harmonic motions with the same frequency act on a particle at right angles i.e., along $x$ and $y$ axis. If the two amplitudes are equal and the phase difference is $\pi / 2$, the resultant motion will be
[1997]
(a) a circle
(b) an ellipse with the major axis along y-axis
(c) an ellipse with the major axis along $x$-axis
(d) a straight line inclined at $45^{\circ}$ to the $x$-axis
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Answer:
Correct Answer: 16.(a)
Solution:
- (a) Equation of two simple harmonic motions
$ \begin{align*} & y=A \sin (\omega t+\phi) \tag{1}\\ & x=A \sin (\omega t+\phi+\frac{\pi}{2}) \\ & \Rightarrow x=A \cos (\omega t+\phi) \tag{2} \end{align*} $
On squaring and adding equations (1) and (2), $x^{2}+y^{2}=A^{2}$
This is an equation of a circle. Hence, resulting motion will be a circular motion.
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