Question

On applying forced vibrations, the resonance wave becomes very fast when

Answer 1

Forced vibration

1. Such vibration where a body or a system is made to vibrate under the action of a strong impressed periodic force with a frequency equal to that of the impressed force, which is different from the natural frequency of the system, is called forced vibration.
2. We know that the amplitude of forced vibration is defined by the form, $a=\frac{f_o}{2k\omega }$, where, $f_o=\frac{F_o}{m}$($F_o$ is the driving force at time zero and m is the mass of the oscillator), $k$ is the damping coefficient, and $\omega$ is the frequency.

Diagram

Amplitudes at resonance

1. As we know, the amplitude of resonance is inversely proportional to the damping coefficient $k$, amplitude, $a=\frac{f_o}{2k\omega }$.
2. Resonance will fast when amplitude will maximum. The amplitude will be maximum when the damping coefficient will minimum.
3. So, at $k$$=0$, $a=\infty$ i.e. if we decrease the damping force, the resonance wave becomes very fast.

On applying forced vibrations, the resonance wave becomes very fast when the damping force is small.