| Two simple harmonic motions, as shown, are at right angles. They are combined to form Lissajous figures. |
| \[x(t)=A\sin (at+\delta )\] |
| \[y(t)=B\sin (bt)\] |
| Identify the correct match below [JEE Online 15-04-2018 (II)] |
A) \[\text{Parameters: A=B, a=2b;}\delta \text{=}\frac{\pi }{2};Curve:Circle\]
B) \[\text{Parameters: A=B, a=b;}\delta \text{=}\frac{\pi }{2};Curve:line\]
C) \[\text{Parameters: A}\ne \text{B, a=b; }\delta \text{=}\frac{\pi }{2};Curve:\text{Ellipse}\]
D) \[\text{Parameters:}A\ne B,a=b;\delta =0;\text{Curve : Parabola}\]
Correct Answer: C
Solution :
| [c] Lissajous curves take common shapes depending on the variables in the expressions. |
| \[x=A\sin (at+\delta )\] |
| \[y=B\sin (bt+r)\] |
| If \[A\ne B\And a=b\] we obtain ellipse |
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