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A block-spring system can perform free undamped oscillation at angular frequency omega1. With weak damping present it performs damped SHM at angular frequency omega2. When driven by a sinusoidal force (damping still present), its forced-oscillation amplitude peaks at angular frequency omega3. The correct ordering is:

1. omega1 > omega2 > omega3
2. omega1 > omega2 = omega3
3. omega1 = omega2 = omega3
4. omega1 > omega3 > omega2

Correct answer: omega1 > omega2 > omega3

Solution

omega1 = omega0 (natural). Damped omega2 = sqrt(omega0² - b²) < omega1. Amplitude resonance omega3 = sqrt(omega0² - 2b²) < omega2. So omega1 > omega2 > omega3.

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