A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force Fsin ω t. If the amplitude of the particle is maximum for ω = ω₁ and the energy of the particle is maximum for ω = ω₂, then (where ω₀ → natural angular frequency of oscillations of particle) (a) ω₁ = ω₀ and ω₂ ≠ ω₀ (b) ω₁ = ω₀ and ω₂ = ω₀ (c) ω₁ ≠ ω₀ and ω₂ = ω₀ (d) ω₁ ≠ ω₀ and ω₂ ≠ ω₀

Answer: (c). Amplitude resonance occurs at ω₁ = √(ω₀² - (b²)/(2m²)), slightly below ω₀, so ω₁ ≠ ω₀. Velocity amplitude, and hence kinetic energy, is maximum exactly at ω₂ = ω₀. So the answer is (c).

A particle, with restoring force proportional to displacement and… | NEET 1998 (AIPMT)

Q28NEET 1998 · AIPMTEasy

Damped, Forced Oscillations & Superposition

A particle, with restoring force proportional to displacement and resisting force proportional to velocity is subjected to a force $F\sin\omega t$ . If the amplitude of the particle is maximum for $\omega = \omega_1$ and the energy of the particle is maximum for $\omega = \omega_2$ , then

(where $\omega_0 \rightarrow$ natural angular frequency of oscillations of particle)

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Answer: (c)

Amplitude resonance occurs at $\omega_1 = \sqrt{\omega_0^2 - \frac{b^2}{2m^2}}$ , slightly below $\omega_0$ , so $\omega_1 \neq \omega_0$ .
Velocity amplitude, and hence kinetic energy, is maximum exactly at $\omega_2 = \omega_0$ .
So the answer is (c).

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Damped, Forced Oscillations & Superposition question from NEET 1998 (AIPMT)

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