When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is :
Solution
Since, the particle is executing SHM.<br/><br/>Therefore, displacement equation of wave will be<br/><br/>$y = A\sin \omega t$<br/><br/>$\Rightarrow y/A = \sin \omega t$<br/><br/>and wave velocity equation will be<br/><br/>${v_y} = {{dy} \over {dt}} = A\omega \cos \omega t$<br/><br/>$\Rightarrow {v_y}/A\omega = \cos \omega t$<br/><br/>Now, ${\sin ^2}\omega t + {\cos ^2}\omega t = 1$<br/><br/>$\therefore$ ${(y/A)^2} + {({v_y} / A\omega )^2} = 1$<br/><br/>This equation is similar to the equation of ellipse.
About this question
Subject: Physics · Chapter: Oscillations · Topic: Simple Harmonic Motion
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