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# Tag Info

### Why does the eigenvalues of an angular frequency matrix are the natural frequency? (INTUITION)

The acceleration is the second derivative of the position i.e. $a \equiv \ddot{x}$. This means that the you have managed to decompose the couple system of oscillators into independent modes (to state ...

### Structural dynamics: Why are modeshape-vectors referred to as orthogonal?

No reference I encountered on the topic so far so has called the eigenmodes orthogonal with respect to the standard scalar product, for the obvious reason you point out: They are not orthogonal in ...

### Calculating eigenvalues and eigenstates of an infinite dimensional Hamiltonian

Here is an alternative, more direct method of determining eigenstates and eigenvalues (the situation is complicated by the fact that the eigenstates are not normalisable - see (3) in Tobias Fünke's ...
The following procedure is only on a formal level. Let $k\in [-\pi,\pi)$ and define $$|k\rangle :=\frac{1}{\sqrt{2\pi}}\sum\limits_{m\in\mathbb Z} e^{ikm}|m\rangle \tag 1 \quad .$$ Note that \$|k\...