In forced oscillation of a particle the amplitude is maximum for a frequency $\omega_{1}$ of the force, while the energy is maximum for a frequency $\omega_{2}$ of the force, then

(C) $\omega_{1} \omega_{2}$ when damping is large

JEE Main · 2004 · 24 Apr 2004 · Offline · Elasticity & SHM

In forced oscillation of a particle the amplitude is maximum for a frequency

ω_{1}

of the force, while the energy is maximum for a frequency

ω_{2}

of the force, then

(A) $ω_{1} = ω_{2}$ ✓ Correct
(B) $ω_{1} > ω_{2}$
(C) $ω_{1} < ω_{2}$ when damping is small and $ω_{1} > ω_{2}$ when damping is large
(D) $ω_{1} < ω_{2}$

Answer: (A)

Solution

Both the amplitude and the energy of a driven oscillator reach their greatest value when the driving frequency is tuned to the natural frequency of the system, the condition we call resonance. The frequency that maximises the amplitude and the one that maximises the energy are one and the same, so

ω_{1} = ω_{2}

JEE Main · 2004 · 24 Apr 2004 · Offline · Single correct option

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