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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 π/2, the resultant motion will be
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- a circle
- an ellipse with the major axis along y-axis
- an ellipse with the major axis along x-axis
- a straight line inclined at 45° to the x-axis
Correct Option: A
Equation of two simple harmonic motions
y = A sin (ωt + φ) .....................(1)
| x = A sin |  | ωt + φ + |  | ||
| 2 |
⇒ x = A cos (ωt + φ) .....................(2)
On squaring and adding equations (1) and (2), x2 + y2 = A2
This is an equation of a circle. Hence, resulting motion will be a circular motion.
