The total energy of a simple harmonic oscilla | vedclass

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(C) The total energy of a simple harmonic oscillator is given by $E = \frac{1}{2}m\omega^2 a^2$,where $a$ is the amplitude.The kinetic energy $K$ at a

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$3E/4$

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(C) The total energy of a simple harmonic oscillator is given by $E = \frac{1}{2}m\omega^2 a^2$,where $a$ is the amplitude.The kinetic energy $K$ at any displacement $y$ is given by $K = \frac{1}{2}m\omega^2(a^2 - y^2)$.Given that the displacement is half the amplitude,$y = a/2$.Substituting this into the kinetic energy formula:$K = \frac{1}{2}m\omega^2(a^2 - (a/2)^2)$$K = \frac{1}{2}m\omega^2(a^2 - a^2/4)$$K = \frac{1}{2}m\omega^2(3a^2/4)$$K = \frac{3}{4}(\frac{1}{2}m\omega^2 a^2)$Since $E = \frac{1}{2}m\omega^2 a^2$,we get:$K = \frac{3}{4}E$.

The total energy of a simple harmonic oscillator is $E$. What is its kinetic energy at half the amplitude?

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