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A mass-spring system of mass m and spring constant K is driven by a periodic force F0*cos(omega*t). The natural frequency is omega0 = sqrt(K/m) and the forced oscillation amplitude is A = F0 / sqrt(m²*(omega0² - omega²)² + (b*omega)²), where b is the damping coefficient. Which of the following statement(s) is/are true? (A) The amplitude increases as the driving frequency omega approaches omega0. (B) If the damping coefficient b is increased, the maximum amplitude of oscillation also increases. (C) The phase difference phi between the driving force and the velocity of the mass depends on both omega and b.

1. (A) The amplitude increases as the driving frequency approaches the natural frequency omega0.
2. (B) If the damping coefficient is increased, the maximum amplitude of oscillation will also increase.
3. (C) The phase difference phi between the driving force and the velocity of mass depends on both the driving frequency omega and the damping coefficient b.
4. (D) All statements are true

Correct answer: (A) The amplitude increases as the driving frequency approaches the natural frequency omega0.

Solution

As omega -> omega0 the amplitude rises (A true). Increasing b reduces A_max = F0/(b*omega0) (B false). The phase of velocity w.r.t. force = arctan[(m*(omega0²-omega²))/(b*omega)] depends on both omega and b (C true). So A and C are true.

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