Question

In resonance frequency of external periodic force is equal to its natural frequency of vibration is it correct?​

Answer 1

• Resonance occurs when the frequency of the applied force becomes nearly equal to the natural frequency of vibration of the body. During resonance the amplitude of the forced vibration reaches its maximum value

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Answer 2

Answer:

This statement is partially correct.

This is Velocity Resonance when the frequency of external force coincide with the natural frequency of the vibrating system.

Explanation:

Forced Vibration:

If a vibrating system is subjected to a external periodic force it is said to be in forced vibration. The body tends to vibrate with it's own frequency (ω) while the applied force tries to impose it's frequency (p) on it. Soon the natural vibration of the system die-out due to the damping forces of the resistive medium and ultimately the vibration with a frequency same of impressed force will continue. Such vibration is called Forced Vibration.

Resonance:

There is two types of resonance in Forced Vibration:

1. Velocity Resonance
2. Amplitude Resonance

Amplitude Resonance:

For a certain value of frequency of external periodic force (p) the amplitude (A) of the oscillating system get it's maximum value. This is called amplitude resonance.

$p = \sqrt{\omega ^{2}-2b^{2} }$

b = damping co-efficient

Velocity Resonance:

When the frequency of external force (p) coincide with the natural frequency (ω) of the vibrating system the energy of the system (E) get it's maximum value. This phenomenon is called the velocity resonance.

Here in this case;

$External frequency = Natural frequency\\p =\omega$

It means the amplitude resonating frequency is slightly smaller than the velocity resonating frequency or the natural frequency.

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