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  4. A particle is executing SHM. Then, the graph of velocity as a function of displacement is a/an

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Q. A particle is executing SHM. Then, the graph of velocity as a function of displacement is a/an

CMC MedicalCMC Medical 2007

Solution:

From the relation, $ {{v}^{2}}={{\omega }^{2}}({{a}^{2}}-{{x}^{2}}) $ $ \Rightarrow $ $ {{v}^{2}}+{{\omega }^{2}}{{x}^{2}}={{\omega }^{2}}{{a}^{2}} $ $ \Rightarrow $ $ \frac{{{v}^{2}}}{{{a}^{2}}{{\omega }^{2}}}+\frac{{{x}^{2}}}{{{a}^{2}}}=1 $ which is the equation of an ellipse.