The correct option is D 4π5 s
Given , mass of the particle m=2 kg
Potential energy as a function of the position of particle is given by
U=12mω2x2
At extreme positions, x=±A. From the data given in the diagram, we can say that
U=12mω2A2⇒12mω2(0.4)2=1.0 J
⇒ω=√2×1.0(0.4)2×2=2.5 rad/s
Time period of oscillation of a particle executing SHM is given by,
T=2πω
∴T=2π2.5=4π5 s
Thus, option (d) is the correct answer.