A 5 kg mass bounces in simple harmonic motion at the end of a spring. At which point is the acceleration of the mass the greatest?
Correct answer: A. When the spring is fully compressed and when the spring is fully extended
- A. When the spring is fully compressed and when the spring is fully extended
- B. When the spring is at its rest length
- C. When the spring is halfway between its rest length and its fully extended or compressed length
- D. The acceleration is constant
Explanation
In SHM acceleration a = −ω² x, so its magnitude is proportional to displacement |x|. The extremes (maximum compression/extension) have the largest |x|, hence largest magnitude of acceleration. At equilibrium acceleration is zero.
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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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