A damped spring-mass system is forced to oscillate at t = 0 by the application of an impulse force. Which of the following are true?

Correct option is B

​$$\begin{aligned}&\textbf{1. Damping Ratio } (\zeta): \\&\quad \circ\ 0 < \zeta < 1: \textbf{Underdamped} \ (\text{oscillations with exponential decay}) \\&\quad \circ\ \zeta = 1: \textbf{Critically damped} \ (\text{fastest return to equilibrium without oscillations}) \\&\quad \circ\ \zeta > 1: \textbf{Overdamped} \ (\text{no oscillations, slow return to equilibrium}) \\&\quad \circ\ \zeta < 0: \textbf{Unstable} \ (\text{oscillations grow exponentially}) \\[1em]&\textbf{2. Impulse Response:} \\&\quad \text{An impulse force imparts initial energy, causing transient oscillations} \\&\quad \text{or decay depending on } \zeta.\end{aligned}$$

Correct answer - "If the damping ratio is between 0 and 1, the system will eventually come to rest". The oscillations decay exponentially, so the system will eventually settle at equilibrium.​​