Is the Damped Vibration Period Constant?

[ORemington]

Damped vibration period remains constant. Introduction to Damped Vibration Period: The motion of a particle cannot completely repeat itself after a certain period of time; damped vibration is not a periodic motion. State Introduction: Underdamped State: When 0<ζ<1, the solution is a pair of complex conjugate roots with negative real parts, and the system's time response exhibits oscillatory characteristics, known as the underdamped state. Critical Damping: When ζ=1, the solution is a pair of repeated real roots, and the damping form of the system is called critical damping. In real life, many doors in buildings, such as those in rooms or bathrooms, are equipped with torsion springs for automatic closing and corresponding damping hinges to make the door's damping close to critical damping, ensuring that closing the door or wind-induced movement does not create excessive noise.