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For the forced oscillations of a particle, the amplitude of oscillation is largest at a driving frequency omega1, while the power absorbed is largest at a driving frequency omega2. Which relation is correct?
- omega1 < omega2
- omega1 = omega2
- omega1 > omega2
- omega1 < omega2 for small damping and omega1 > omega2 for large damping
Correct answer: omega1 < omega2
Solution
Maximum power transfer (velocity/energy resonance) occurs at the natural frequency omega0, so omega2 = omega0. The amplitude maximum occurs at omega1 = sqrt(omega0² - 2*b²) (where b is the damping parameter), which is slightly less than omega0. Hence omega1 < omega2.
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