Question

Represent graphically the variations of K.E., P.E. and T.E. of a particle performing linears S.H.M. with respect to displacement.

Answer 1

Explanation:

Represent graphically the variations of K.E., P.E. and T.E. of a particle performing linears S.H.M. with respect to displacement.

Represent graphically the variations of K.E., P.E. and T.E. of a particle performing linears S.H.M. with respect to displacement.

Answer 2

Graphical Representation of KE, TE & PE in SHM

The general equation of various energy contents of a particle performing simple harmonic motion can be stated as :

• PE is potential energy
• TE is total energy
• KE is kinetic energy

Now, the equations are :

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

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

$3)\: TE = KE + PE$

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

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

$\implies\: TE = constant$

• m is mass
• $\omega$ is angular frequency
• x is displacement
• a is amplitude

Hence, the graphs will be as attached.