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(B) The total mechanical energy $E$ of a $SHM$ oscillator is given by $E = \frac{1}{2} k A^2$,where $k$ is the force constant and $A$ is the amplitude

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$v_{\max} = \sqrt{\frac{2E}{m}}$

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(B) The total mechanical energy $E$ of a $SHM$ oscillator is given by $E = \frac{1}{2} k A^2$,where $k$ is the force constant and $A$ is the amplitude.Since $k = m \omega^2$,we can write $E = \frac{1}{2} m \omega^2 A^2$.We know that the maximum velocity $v_{\max}$ of a $SHM$ oscillator is given by $v_{\max} = \omega A$.Substituting this into the energy equation: $E = \frac{1}{2} m (\omega A)^2 = \frac{1}{2} m v_{\max}^2$.Rearranging for $v_{\max}$,we get $v_{\max}^2 = \frac{2E}{m}$.Therefore,$v_{\max} = \sqrt{\frac{2E}{m}}$.

Write the maximum velocity of a $SHM$ oscillator in terms of mechanical energy $E$ and mass of oscillator $m$.

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