Draw a graph to show the variation of PE, KE and total energy of a simple harmonic oscillator with displacement.

Hint: Apply the formulae of PE and KE in SHM.
Step 1: Find the potential energy of SHM.
The potential energy (PE) of a simple harmonic oscillator is
                       =12kx2=12mω2x2                                  ...(i)
Where k=force constant =mω2
When PE is plotted against displacement x, we will obtain a parabola.
When x =0, PE =0
When x=±A, PE= maximum=12mω2A2
Step 2: Find the KE of SHM.
KE of a simple harmonic oscillator= 12mv2                                        [v=ωA2-x2]
                                                 =12mωA2-x22
=12mω2(A2-x2)                                              ...(ii)
This is also a parabola if plot KE against displacement x.
i.e.,                       KE=0 at x=±A
and                      KE=12mω2A2 at x=0
Step 3: Find the total energy of SHM.
Now, the total energy of the simple harmonic oscillator = PE+KE      [using Eqs. (I) and (ii)]
                     =12mω2x2+12mω2(A2-x2)
=12mω2x2+12mω2A2-12mω2x2
TE=12mω2A2
Which is constant and does not depend on x.
Plotting under the above guidelines KE, PE and TE versus displacement x-graph as follows: