By: Tao Steven Zheng (鄭濤)

【Problem】

Consider the position function . Show that this function solves the differential equation

and determine the value of in terms of .

【Solution】

Take two time derivatives:

Consequently,

Divide away :

Therefore, .

This quantity is the angular frequency of the wave. Mathematically speaking, it is the eigenvalue of the differential equation.

【Physics Principle】

Note that the above differential equation is derived from the mass on a spring model.