For what value of displacement the kinetic en | vedclass

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(C) The kinetic energy $(KE)$ of a simple harmonic oscillator is given by $KE = \frac{1}{2} m \omega^{2}(A^{2} - x^{2})$.The potential energy $(PE)$ i

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$x=\pm \frac{A}{\sqrt{2}}$

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(C) The kinetic energy $(KE)$ of a simple harmonic oscillator is given by $KE = \frac{1}{2} m \omega^{2}(A^{2} - x^{2})$.The potential energy $(PE)$ is given by $PE = \frac{1}{2} m \omega^{2} x^{2}$.Setting $KE = PE$:$\frac{1}{2} m \omega^{2}(A^{2} - x^{2}) = \frac{1}{2} m \omega^{2} x^{2}$.Canceling the common terms $\frac{1}{2} m \omega^{2}$ from both sides:$A^{2} - x^{2} = x^{2}$.Rearranging the terms:$2x^{2} = A^{2}$.Solving for $x$:$x^{2} = \frac{A^{2}}{2}$.Therefore,$x = \pm \frac{A}{\sqrt{2}}$.

For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?

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