Directions : In the following question more than one of the answers given may be correct. Select the correct answer and mark it according to the code:
If two orthogonal SHM of same frequency having initial phase difference of n/2 acts simultaneously on a particle free to move, the particle can move in a (1) straight line (2) circle (3) parabola (4) ellipseA) 1, 2 and 3 are correct
B) 1 and 2 are correct
C) 2 and 4 are correct
D) 1 and 3 are correct
Correct Answer: C
Solution :
\[x=a\sin \omega t\]and \[y=b\sin \left( \omega t+\frac{\pi }{2} \right)\] \[=b\cos \omega t\] \[\therefore \]\[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}={{\sin }^{2}}\omega t+{{\cos }^{2}}\omega t=1\] It is an equation of ellipse, if\[a=b,\]then \[\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}}=1\]or \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] It is an equation of circle.
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