Systems with Several Masses

When there is a single mass, its motion has only one degree of freedom and one natural mode of vibration.

Consider the system having 2 masses and 3 springs:

**Figure 6:** 2-mass 3-spring system.
$\begin{figure}\centerline{\scalebox{.9}{% \input{2mass3spring.pstex_t}}}\end{figure}$

The system will have two ``normal'' independent modes of vibration:

one in which masses move in the same direction, with frequency

$\displaystyle f_1 = \frac{1}{2\pi}\sqrt{\frac{K}{m}}$
one in which masses move in different directions with frequency

$\displaystyle f_2 = \frac{1}{2\pi}\sqrt{\frac{3K}{m}}$

(assuming equal masses and springs).

``MUS 206: Mechanical Vibration'' by Tamara Smyth, Department of Music, University of California, San Diego (UCSD).