When the frequency of the forced vibration is equal to the frequency of the free vibration, this condition is called ______.
resonance
Understanding Vibration Concepts
When an object vibrates, it can do so in different ways depending on how it is set into motion and what forces are acting upon it.
- Free Vibration: This occurs when an object vibrates after an initial disturbance, and no external force keeps it going. The frequency at which it vibrates is its natural frequency, determined by its physical properties (like mass and stiffness).
- Forced Vibration: This occurs when an external, oscillating force is continuously applied to an object, causing it to vibrate at the frequency of the applied force.
What is Resonance?
The question asks about the condition when the frequency of the forced vibration is equal to the frequency of the free vibration. This specific condition has a special name in physics and engineering:
When the frequency of the external driving force (in forced vibration) matches the natural frequency of the system (in free vibration), the amplitude of vibration can become very large. This phenomenon is called resonance.
At resonance, even a small driving force can produce large oscillations because energy is transferred efficiently from the driving force to the vibrating system.
Analyzing the Options
Let's look at the given options:
- Vibration excitation: This is a general term for starting a vibration, not the specific condition described.
- Frequency factor: This term is typically used in other contexts, like in rate equations in chemistry, and is not related to the described vibration condition.
- Resonance: As explained above, this is precisely the condition where the forced vibration frequency matches the free vibration frequency.
- Simple harmonic motion: This describes a specific type of oscillatory motion where the restoring force is directly proportional to the displacement, but it doesn't specifically define the condition where forced and free frequencies are equal.
Based on the definitions, the condition where the frequency of the forced vibration is equal to the frequency of the free vibration is called resonance.
Important Questions from Forced Vibration
Which method is used to find the natural frequencies of a system with multi degrees of freedom?
The ratio of the amplitude of the steady-state response of forced vibrations to the static deflection under the action of a static force is known as
The amplitude of the steady-state reaction divided by the static deflection under force application is known as _______.
Consider a forced single degree-of-freedom system governed by \(\rm \ddot x(t) + 2 ζ ω_n \dot x (t) + ω_n^2 x(t) = ω_n^2 \cos (ω t)\), where ζ and ωn are the damping ratio and undamped natural frequency of the system, respectively, while ω is the forcing frequency. The amplitude of the forced steady state response of this system is given by [(1 − r2)2 + (2ζr)2]-1/2, where 𝑟 = ω/ω n. The peak amplitude of this response occurs at a frequency ω = ωp. If ωd denotes the damped natural frequency of this system, which one of the following options is true?
The amplitude ratio of two successive oscillations of a damped vibratory system is
