Question

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

Answer 1

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 ω_1.

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.