Sketching curved total potential energy against displacement

Question

I am asked to "Sketch a curve of total potential energy against displacement for the mass on the spring."

From previous question I found that the amplitude of the motion is 5.0 m, the frequency is 0.5Hz, the maximum velocity of the mass is 15.71 ms$^-1$ and the maximum acceleration of the mass is 49.35 ms$^-2$.

Using this information I have produced the following graph and curve.

Is this correct ?

Answer 1

The potential energy for a spring is:

$$U_e={1\over2}kx^2$$

so the graph is a parabola (upward).

Your graph represents the displacement of the spring from the equilibrium point, respect to the time.