A mass-spring-damper oscillator representing an aircraft landing gear strut is governed by: $$\frac{d^2 y}{dt^2} + 6 \frac{dy}{dt} + 25 y = 0$$ What is the undamped natural frequency $\omega_n$ (in rad/s) of this oscillatory system?

Answer Key:

5

### 5-Stage Derivation & Analytical Solution: 1. **Stage 1: Canonical Second-Order Form:** $\ddot{y} + 2\zeta\omega_n\dot{y} + \omega_n^2 y = 0$. 2. **Stage 2: Parameter Extraction:** $\omega_n^2 = 25$. 3. **Stage 3: Computation:** $\omega_n = \sqrt{25} = 5\text{ rad/s}$. 4. **Stage 4: Output:** 5.

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