Differential Equations

Consider the ODE $\frac{d^2 y}{dx^2} + 2\zeta \omega_n \frac{dy}{dx} + \omega_n^2 y = 0$. Which of the following statements are TRUE?

Options:

• (A) If $\zeta > 1$, the system is overdamped with two distinct real roots
• (B) If $\zeta = 1$, the system is critically damped with repeated real roots
• (C) If $0 < \zeta < 1$, the system is underdamped with complex conjugate roots
• (D) If $\zeta = 0$, the system undergoes undamped harmonic oscillation