Draw a graph to show the variation of P.E., K.E. and total energy of a simple harmonic oscillator with displacement.

Total energy of S.H.M is constant, ∴ we get a straight line

Kinetic energy for the simple harmonic motion is given as,

where x = displacement

ω = angular velocity

m = mass of the system

a = amplitude

the above equation is an equation of the downward opening parabola symmetric along y-axis and vertex at on y-axis

Potential energy for the simple harmonic motion is given as,

where x = displacement

ω = angular velocity

m= mass of the system

a = amplitude

the above equation is an equation of the upward opening parabola symmetric along y-axis and vertex at (0,0) on y-axis

∴ following is the graph we get,