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For the forced-vibration responses of a TDOF system, what does it mean physically when the determ...

For the forced-vibration responses of a TDOF system, what does it mean physically when the determinant of the matrix equation

For the forced-vibration responses of a TDOF system, what does it mean physically when the determinant of the matrix equation becomes zero? xiv.
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If determinant equals to zero means here we get natural frequency as a normal modes.

Example:

Examining the first normal mode. an oscillation occurs at an oscillation frequency ω1.Since the central spring does not deform, and the two masses oscillate, each on a single spring, thus giving a frequency ω1.

The second normal mode has a frequency ω2 thus the masses move in opposite directions, and the frequency of oscillation is increased.

If such a system was at rest, and an initial impulse was given to one of the masses, both modes would be excited.

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