Question

In forced oscillation of a particle the amplitude is maximum for a frequency ω₁ of force, while the energy Is maximum for a frequency ω₂ of the force, then:

• A. ω1 > ω2
• B. ω1 < ω2
• C. ω1 = ω2
• D. None f these.

Answer 1

The correct option is C

ω1 = ω2

Forced vibration

1. The vibration of a body dies out with time due to the dissipation of energy.
2. If some external periodic force is constantly applied to the body, it continues to oscillate under the influence of such external forces. Such vibrations of the body are called forced vibrations.

Energy and amplitude at resonance

1. We know that at the resonance of forced vibration the energy and amplitude reach their maximum point.
2. When the frequency of the force vibration is the same as the object's natural frequency, then resonance occurs.
3. Resonance will be possible, when ${\omega }_1={\omega }_2$.

Therefore, energy will be maximum when ${\omega }_1={\omega }_2$.

Hence, option (C) is correct.