Energy in Simple Harmonic Motion

A particle of mass $m$ oscillates in Simple Harmonic Motion between points $x_1$ and $x_2$, the equilibrium position being $O$. Which of the following graphs represents the variation of its potential energy $\left(U\right)$ with respect to its position?

A particle executing SHM with an amplitude $\mathrm{A}$. The displacement of the particle when its potential energy is half of its total energy is

Graph of kinetic energy in terms of displacement in $SHM$ :-

(i) At what displacement of particle executing $SHM,$ has maximum kinetic energy.

A particle of mass m executing SHM with amplitude $A$ and angular frequency $\mathrm{\omega }$. The average value of the kinetic energy and potential energy over a period is

For a particle executing SHM the displacement $x$ is given by $x=A\cos \omega t.$ Identify the graph which represents the variation of potential energy ($PE$) as a function of time and displacement$x$.

A particle free to move along the $\mathrm{X}$-axis has potential energy given as $U\left(x\right)=k\left[1-\exp \left(-x^2\right)\right] (\text{for} -\infty \le x\le +\infty )$, where $k$ is a positive constant of appropriate dimensions. Then

A body executes simple harmonic motion. The potential energy (PE), the kinetic energy (KE) and total energy (TE) are measured as function of displacement $x$. Which of the following statement is true?

A body is executing simple harmonic motion. If the bottom datum is at mean position, then

For a particle executing SHM, the displacement $x$ is given by $x=A\cos \left(\omega t\right)$. Identify the graph which represents the variation of potential energy $\left(\mathrm{PE}\right)$ as a function of time and displacement $x$.

For a particle executing $S.H.M.$ the displacement $x$ is given by $x=A\cos \left(\omega t\right)$. Identify the graph which represents the variation of potential energy $\left(PE\right)$ as a function of time $t$ and displacement $x$. 
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In a simple harmonic oscillator, at the mean position