In a damped forced oscillation, when the damping coefficient b is increased, how does the resonant frequency omega_r compare to the natural frequency omega₀?

(A) omega_r = omega₀
(B) omega_r < omega₀
(C) omega_r > omega₀
(D) omega_r is independent of b

Correct answer: (B) omega_r < omega₀

Solution

For a driven damped oscillator, amplitude is maximum at omega_r = sqrt(omega₀² - b²/(2m²)). Since b²/(2m²) > 0, omega_r < omega₀ always, and increasing b makes omega_r smaller.

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