Damped natural frequency isa)same as natural frequencyb)lower than natural frequencyc)higher than natural frequencyd)none of the aboveCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

If a resonant mechanical structure is set in motion and left to its own devices, it will continue to oscillate at a particular frequency known as its natural frequency, or "damped natural frequency". This will be a little lower in frequency than the resonant frequency, which is the frequency it would assume if there were no damping. The resonant frequency is also called the "undamped natural frequency”

Answer

Damped Natural Frequency

If a resonant mechanical structure is set in motion and left to its own devices, it will continue to oscillate at a particular

frequency

known as its

natural frequency

, or 'damped natural frequency'. This will be a little lower in frequency than the

resonant frequency

, which is the frequency it would assume if there were no

damping

. The resonant frequency is also called the 'undamped natural frequency

Answer

Damped natural frequency is lower than natural frequency because of the presence of damping in a system. To understand this concept, let's break down the answer into headings and key points.

1. Natural Frequency:
- Natural frequency refers to the frequency at which a system oscillates when no external forces act upon it.
- It depends on the mass and stiffness of the system and is often denoted by the symbol ω (omega).
- Natural frequency is determined by the equation ω = √(k/m), where k is the stiffness of the system and m is the mass.

2. Damped Natural Frequency:
- Damping is the mechanism that dissipates energy from a vibrating system, causing the amplitude of the oscillations to decrease over time.
- Damped natural frequency refers to the frequency at which a damped system oscillates.
- The presence of damping alters the behavior of the system and reduces its natural frequency.
- Damping is represented by a damping ratio, often denoted by the symbol ζ (zeta).
- The damped natural frequency, denoted by ωd (omega_d), is given by the equation ωd = ω * √(1 - ζ^2), where ω is the natural frequency and ζ is the damping ratio.

3. Relationship between Natural Frequency and Damped Natural Frequency:
- The damping ratio (ζ) affects the damped natural frequency (ωd) of a system.
- When the damping ratio is zero (no damping), the damped natural frequency is equal to the natural frequency (ωd = ω).
- As the damping ratio increases, the damped natural frequency decreases.
- When the damping ratio is high, close to or above 1, the damped natural frequency becomes significantly lower than the natural frequency.
- This is because damping dissipates energy and reduces the amplitude of oscillations, resulting in a lower frequency.

Conclusion:
In conclusion, the damped natural frequency is lower than the natural frequency because damping reduces the amplitude of oscillations and alters the behavior of the system. The presence of damping in a system decreases the damped natural frequency compared to the natural frequency.

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