Physical systems – example exhibiting underdamped behavior Which of the following is a typical real-world example of an underdamped dynamic system?

Introduction / Context:
Underdamped systems exhibit oscillatory transients that decay over time. Recognizing such systems in process and instrumentation helps in sensor selection, controller tuning, and interpretation of step tests. This question asks you to pick a canonical underdamped example from common equipment.

Given Data / Assumptions:

• Underdamped response: oscillations with decaying amplitude after a disturbance.
• Overdamped/first-order response: monotone approach to steady state.
• Examples span fluid-filled instruments, thermal sensors, and reactors.

Concept / Approach:
A U-tube manometer behaves like a mass–spring–damper: the oscillating liquid columns (inertia), gravity (restoring force), and viscous/frictional losses (damping). When disturbed by a step in pressure, the liquid level oscillates about the equilibrium and decays depending on damping—an archetypal underdamped response. In contrast, a thermocouple in a thermowell shows a sluggish, non-oscillatory rise (often well-modeled as second-order overdamped or as a sum of first-order lags). A CSTR with a first-order reaction is typically a first-order or overdamped higher-order system with no oscillation. A spring-loaded diaphragm valve in quasi-static use usually exhibits non-oscillatory displacement for small steps (unless actuator dynamics and fluid forces introduce resonance, which is not the typical foundational example).

Step-by-Step Solution:

Verification / Alternative check:
Manometer transient derivations yield a second-order ODE with natural frequency and damping ratio; experiments show classic ring-down behavior.

Why Other Options Are Wrong:

• Thermowell thermocouple: Overdamped (sum of lags), no ringing.
• CSTR first-order: Monotonic, no oscillation.
• Spring-loaded diaphragm valve: Typically dominated by static compliance and damping; oscillations are not the fundamental textbook case.

Common Pitfalls:
Assuming any mechanical device oscillates; damping often suppresses oscillations unless inertia and restoring forces form a clear second-order pair.

Final Answer:
U-tube manometer