A mass-spring system is driven at a frequency f = 3 Hz . The natural frequency is f = 2 Hz. What is the ratio of the amplitude at resonance to the amplitude at f (assume light damping)?
Correct answer: C. 2.0
- A. 1.0
- B. 1.5
- C. 2.0
- D. 3.0
Explanation
The amplitude ratio is given by Aresonance / A(fd) = fo / |fd-fo| , 2/ |3-2| = 2. However, considering light damping and practical scenarios, the ratio is often approximated as fo / Δf = 2/1 = 2.
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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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