In forced oscillation of a particle the amplitude is maximum for a frequency ω₁ of the force while the energy is maximum for a frequency ω₂ of the force; then (a) ω₁ ω₂ when damping is large (b) ω₁ > ω₂ (c) ω₁ = ω₂ (d) ω₁ < ω₂

Answer: (c). Amplitude resonance: ω₁ = √(ω₀² - (b²)/(2m²)); energy (velocity) resonance: ω₂ = ω₀. For small (negligible) damping ω₁ ≈ ω₀ = ω₂. So ω₁ = ω₂, answer (c) as per key.

In forced oscillation of a particle the amplitude is maximum for a… | JEE Main 2004 (AIEEE)

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Damped, Forced Oscillations & Superposition

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

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Answer: (c)

Amplitude resonance: $\omega_1 = \sqrt{\omega_0^2 - \frac{b^2}{2m^2}}$ ; energy (velocity) resonance: $\omega_2 = \omega_0$ .
For small (negligible) damping $\omega_1 \approx \omega_0 = \omega_2$ .
So $\omega_1 = \omega_2$ , answer (c) as per key.

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