A damped harmonic oscillator has mas m = 0.4 kg, spring constant k = 200 N/m, and damping coefficient b = 4 kg/s. What fraction of the initial energy remains after one oscillation?
Correct answer: A. 36.8%
- A. 36.8%
- B. 63.2%
- C. 13.5%
- D. 86.5%
Explanation
Energy decays as E = E₀ e(-b/m*t).For one cycle (T = 2π / ω), the fraction remaining is e-b/m*t ≈ e-2π*b/mω0 ≈ 0.368 or 36.8%.
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About Simple Harmonic Motion
Simple harmonic motion is oscillation in which acceleration is directly proportional to displacement and directed toward the equilibrium position. Work includes displacement, velocity, acceleration, phase, period, frequency, amplitude and energy, with applications to springs and simple pendulums. The restoring force and the conditions for SHM distinguish it from general periodic motion.
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