A mass–spring system performs simple harmonic motion with amplitude 10cm and angular frequency ω (value not needed for this question).
(i) On the same set of axes, sketch qualitative graphs of kinetic energy K and potential energy U as functions of displacement x from x=−A to x=+A.
(ii) Explain why the U–x graph is a parabola while the K–x graph is an inverted parabola of the same shape.
(iii) Using the graphs, identify the displacement values at which K=U and state the physical significance of these points.
(iv) Describe how the total energy curve would appear on the same axes and explain its key features.