Question

draw a graph of mechanical energy, kinetic energy and potential energy versus displacement for different position of a motion of a block attached to a spring​

Answer 1

For an SHM:

Kinetic Energy

$\therefore \: KE = \dfrac{1}{2} m { \omega}^{2} \bigg( {a}^{2} - {x}^{2} \bigg)$

Potential Energy:

$\therefore \: PE = \dfrac{1}{2} m { \omega}^{2} \bigg( {x}^{2} \bigg)$

Total energy:

$\therefore \: TE = PE + KE$

$\implies\: TE = \dfrac{1}{2} m { \omega}^{2} \bigg( {a}^{2} - {x}^{2} \bigg) + \dfrac{1}{2} m { \omega}^{2} {x}^{2}$

$\implies\: TE = \dfrac{1}{2} m { \omega}^{2} {a}^{2}$

$\implies\: TE = constant$

Now, refer to attached diagrams.