Draw a graph to show the variation of PE,KE a | vedclass

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(A) For a simple harmonic oscillator,the potential energy $(PE)$ is given by $U = \frac{1}{2} k x^2$,where $x$ is the displacement. This represents a

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Parabolic $PE$ and $KE$ curves with constant total energy line.

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(A) For a simple harmonic oscillator,the potential energy $(PE)$ is given by $U = \frac{1}{2} k x^2$,where $x$ is the displacement. This represents a parabola opening upwards starting from the origin.The kinetic energy $(KE)$ is given by $K = \frac{1}{2} k (A^2 - x^2)$,where $A$ is the amplitude. This represents an inverted parabola.The total energy $(E)$ is the sum of $PE$ and $KE$,which is $E = U + K = \frac{1}{2} k A^2$. This is constant regardless of displacement $x$.On a graph with displacement $x$ on the x-axis and energy on the y-axis:$1$. The $PE$ curve is a parabola $U = \frac{1}{2} k x^2$.$2$. The $KE$ curve is an inverted parabola $K = \frac{1}{2} k (A^2 - x^2)$.$3$. The total energy $E$ is a horizontal straight line at $y = \frac{1}{2} k A^2$.

Draw a graph to show the variation of $PE$,$KE$ and total energy of a simple harmonic oscillator with displacement.

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