Difficulty: Easy
Correct Answer: 180°
Explanation:
Introduction / Context
The phase angle between the steady-state response and the harmonic excitation determines whether the system moves in-phase or out-of-phase with the applied force. Understanding its limiting values helps in mount design and resonance avoidance.
Given Data / Assumptions
Concept / Approach
For force-excited SDOF systems, the phase angle φ is given by tanφ = (2ζr) / (1 − r²). As r increases far above 1, the denominator becomes large negative, so φ → 180° (i.e., the response is almost completely out of phase with the excitation force).
Step-by-Step Solution
Verification / Alternative check
Plotting φ versus r shows φ ≈ 0° for r ≪ 1, φ = 90° at resonance (r ≈ 1), and φ → 180° as r → ∞.
Why Other Options Are Wrong
Common Pitfalls
Final Answer
180°
Discussion & Comments