Consider the position function .
Part 1: Determine the value of if this function solves the differential equation:
Part 2: Try to explain what each term of the above differential equation means.
Take two time derivatives:
Divide away :
This quantity is the angular frequency of the wave. Mathematically speaking, it is the eigenvalue of the differential equation.
Multiply the entire equation by :
Since acceleration is the second time derivative of position
This is Newton’s second law with the spring force being the net force!