仅据平衡位置为系统弹性势能零点就能使振子势能为kx^2/2吗?

CAN THE CONCISE FORM OF kx^2/2 FOR THE SYSTEM POTENTIAL ENEGY BE TAKEN FOR GRANTED IF MERELY THE EQUILIBRIUM POSITION IS CHOSEN AS THE ZERO POINT OF SYSTEM POTENTIAL ENERGY?

为了解题方便,振子势能的kx2/2形式往往被过分地强调.笔者对这种简洁式的隐含条件进行了探究,发现经典说法是"以平衡位置作为系统势能零点",应修改为"平衡位置点、系统势能零点和坐标原点三点重合".文章系统论证了"三点重合"提法的合理性和普适性,通过示例展示了平衡位置参数并不总能在简洁式中被抵消掉.

For the convenience to solve problems, the system potential energy expressed with a concise form of kx2/2 was overemphasized. The condition for ensuring this concise form was explored in this paper. The prevalent assertion is that the point of zero potential energy must situate at the system equilibrium position. However, this assertion will be questioned. It will be argued systematically that for achieving the concise form of kx2/2, three points, the point of zero potential energy, the point of equilibrium and the point of the coordinate system origin, must be coincident with each other. The justification and universality of this three-point coincidence will be articulated. A nontrivial example will be used to illustrate that the static deflection can not always be cancelled out in the concise form.