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A damped harmonic oscillator is described by y = A * e^(-bt/2m) * sin(omega' * t + phi). A mass m = 2 kg is attached to a spring of force constant K = 1250 N/m, and the period of oscillation is T = pi/12 s. Find the damping constant b.

1. 9.8 kg/s
2. 2.8 kg/s
3. 98 kg/s
4. 28 kg/s

Correct answer: 28 kg/s

Solution

omega' = 2*pi/(pi/12) = 24 rad/s. omega0 = sqrt(1250/2) = 25 rad/s. Using omega'² = omega0² - b²/(4m²): 576 = 625 - b²/16, so b² = 49*16 = 784, b = 28 kg/s.

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