Question

For a dynamic system with single degree of freedom, choose the CORRECT statement(s).

• A. Damped natural frequency is greater than the undamped natural frequency.
• B. Dynamic response is always greater than static response at all excitation frequencies.
• C. Damping ratio can be estimated using logarithmic decrement method.
• D. A non-zero phase lag is always observed between the excitation and response for a damped system.

Hint:

Recall how damping changes the natural frequency and how the magnification factor behaves at high frequency ratios.

Answer 1

The Correct Option is C, D

A single degree of freedom system under harmonic excitation is described by its natural frequency, damping ratio and magnification factor, which together set how the response compares with the excitation.

1. Damped natural frequency is greater than undamped natural frequency: Wrong. The relation is \(\omega_d = \omega_n\sqrt{1-\zeta^2}\), so damping always reduces the natural frequency, it never increases it.
2. Dynamic response is always greater than static response at all excitation frequencies: Wrong. The magnification factor drops well below 1 once the excitation frequency goes past about \(\sqrt{2}\) times the natural frequency, so the dynamic response becomes smaller than the static response there.
3. Damping ratio can be estimated using logarithmic decrement method: Correct. The logarithmic decrement, found from the ratio of successive peak amplitudes in free vibration, is a standard experimental way to get the damping ratio.
4. A non-zero phase lag is always observed between excitation and response: Correct. For any damped system with \(\zeta > 0\) responding to a harmonic force, the response always trails the excitation by some phase angle, reaching 90 degrees at resonance.

So the correct options are C and D.