A 1 kg mass oscillates with SHM of amplitude 0.05 m and frequency 2 Hz. What is the total mechanical energy?
Correct answer: B. 0.158 J
- A. 0.079 J
- B. 0.158 J
- C. 0.316 J
- D. 0.474 J
Explanation
Total energy E = ½ k A². Angular frequency ω = 2πf = 2π × 2 = 4π rad/s. k = mω² = 1 × (4π)² ≈ 157.91 N/m. E = ½ × 157.91 × (0.05)² ≈ 0.158 J
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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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