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° to the x-axis
Correct Answer: A
Solution :
The two simple harmonic motions can be given by \[x=a\,\sin \omega t\] ?...(i) and \[y=a\sin \left( \omega t+\frac{\pi }{2} \right)\] \[y=a\,\cos \,\omega t\] ..?.(ii) On squaring and adding Eqs. (i) and (ii), we obtain \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}({{\sin }^{2}}\,\omega t+{{\cos }^{2}}\omega t)\] or \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] This is the equation of a circular motion with radius a. NOTE: Simple harmonic motion is of two types : 1. Linear simple harmonic motion 2. Angular simple harmonic motion
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