Explain and draw the graphs of kinetic energy,potential energy,and mechanical energy versus displacement for $SHM$.

(N/A) For a particle executing $SHM$,the kinetic energy $K(x)$,potential energy $U(x)$,and total mechanical energy $E$ as a function of displacement $x$ are given by:
Kinetic energy: $K(x) = \frac{1}{2} k(A^2 - x^2)$
Potential energy: $U(x) = \frac{1}{2} k x^2$
Mechanical energy: $E = K(x) + U(x) = \frac{1}{2} k A^2$
Where $k$ is the force constant and $A$ is the amplitude.

Displacement $(x)$	Kinetic Energy $(K)$	Potential Energy $(U)$	Mechanical Energy $(E)$
$0$	$\frac{1}{2} k A^2$	$0$	$\frac{1}{2} k A^2$
$\pm A/2$	$\frac{3}{8} k A^2$	$\frac{1}{8} k A^2$	$\frac{1}{2} k A^2$
$\pm A/\sqrt{2}$	$\frac{1}{4} k A^2$	$\frac{1}{4} k A^2$	$\frac{1}{2} k A^2$
$\pm A$	$0$	$\frac{1}{2} k A^2$	$\frac{1}{2} k A^2$

The graph shows that potential energy is a parabola opening upwards,kinetic energy is a downward-opening parabola,and mechanical energy is a constant horizontal line.