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Question

In a simple harmonic oscillator, at the mean position


A
Kinetic energy is minimum, potential energy is maximum
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B
Both kinetic and potential energies are maximum
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C
Kinetic energy is maximum, potential energy is minimum
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D
Both kinetic and potential energies are minimum
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Solution

The correct option is C Kinetic energy is maximum, potential energy is minimum
In $$S.H.M$$, kinetic energy of particle at any point $$P$$ is 
Kinetic energy = $$\displaystyle\frac{1}{2}m\omega^2(a^2 - x^2)$$
Potential energy = $$\left(\displaystyle\frac{1}{2}m\omega^2x^2\right)$$
where $$a$$ is amplitude of particle and $$x$$ is the distance from mean position.
So, at mean position, $$x = 0$$
$$K.E. = \displaystyle\frac{1}{2}m\omega^2a^2$$ (maximum)
$$P.E. = 0$$

Physics

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