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Q. Graph between velocity and displacement of particle, executing SHM is :

MGIMS WardhaMGIMS Wardha 2006

Solution:

Displacement $ y=a\sin \omega t $ Velocity $ v=\omega \sqrt{{{a}^{2}}-{{y}^{2}}} $ Or $ {{v}^{2}}={{\omega }^{2}}({{a}^{2}}-{{y}^{2}}) $ Or $ \frac{{{v}^{2}}}{{{\omega }^{2}}}={{a}^{2}}-{{y}^{2}} $ $ \frac{{{v}^{2}}}{{{\omega }^{2}}{{a}^{2}}}+\frac{{{y}^{2}}}{{{a}^{2}}}=1 $ This is the equation of ellipse.