Consider a simple harmonic motion (SHM). Let | vedclass

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(D) The potential energy $U$ of a body performing $SHM$ is given by $U = \frac{1}{2} k x^2$,where $x$ is the displacement from the mean position.Given

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$\frac{K}{U}=3$

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(D) The potential energy $U$ of a body performing $SHM$ is given by $U = \frac{1}{2} k x^2$,where $x$ is the displacement from the mean position.Given that the displacement $x = \frac{a}{2}$,where $a$ is the amplitude:$U = \frac{1}{2} k \left(\frac{a}{2}\right)^2 = \frac{1}{2} k \frac{a^2}{4} = \frac{1}{8} k a^2$ ... $(i)$The kinetic energy $K$ of the body is given by $K = \frac{1}{2} k (a^2 - x^2)$.Substituting $x = \frac{a}{2}$:$K = \frac{1}{2} k \left(a^2 - \frac{a^2}{4}\right) = \frac{1}{2} k \left(\frac{3 a^2}{4}\right) = \frac{3}{8} k a^2$ ... (ii)Taking the ratio of kinetic energy to potential energy:$\frac{K}{U} = \frac{\frac{3}{8} k a^2}{\frac{1}{8} k a^2} = 3$.

Consider a simple harmonic motion $(SHM)$. Let $K$ and $U$ be kinetic energy and potential energy when the displacement in $SHM$ is one-half $\left(\frac{1}{2}\right)$ the amplitude. Which of the following statements is correct?

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