**Problem**

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.

**Solution**

**Part 1**

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.

**Part 2**

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!

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