The velocity of a particle in simple harmonic | vedclass

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(B) The displacement of a particle in simple harmonic motion is given by $y = A \sin(\omega t)$,where $A$ is the amplitude and $\omega$ is the angular

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$\omega \sqrt {A^2 - y^2} $

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(B) The displacement of a particle in simple harmonic motion is given by $y = A \sin(\omega t)$,where $A$ is the amplitude and $\omega$ is the angular frequency.Differentiating the displacement with respect to time $t$ gives the velocity $v$:$v = \frac{dy}{dt} = A \omega \cos(\omega t)$Using the trigonometric identity $\cos(\omega t) = \sqrt{1 - \sin^2(\omega t)}$,we substitute $\sin(\omega t) = \frac{y}{A}$:$v = A \omega \sqrt{1 - (\frac{y}{A})^2}$Simplifying the expression:$v = A \omega \sqrt{\frac{A^2 - y^2}{A^2}}$$v = A \omega \frac{\sqrt{A^2 - y^2}}{A}$$v = \omega \sqrt{A^2 - y^2}$Thus,the velocity of the particle at displacement $y$ is $\omega \sqrt{A^2 - y^2}$.

The velocity of a particle in simple harmonic motion at displacement $y$ from the mean position is

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