It is given that motion is free simple harmonic motion.
Consider a spring mass system performing free simple harmonic motion.
Displacement of mass is given as
x=x0sinωt The potential energy stored in spring for displacement x can be given as
PE=kx2 Substituting the value of x, we get
PE=kx02sin2ωt Here, k is spring constant and
x0 is also constant.
PE=Csin2ωt (∴C=kx02) Simplify the value of
sin2 ωt, we get
PE=C[] The value of function cos2ωt will always lies between −1 and 1.
Thus, the value of potential energy will be greater than or equal to zero.
0 ≤ PE
This condition is only satisfies by graph (d).