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 is fully extended or compressed length
- D. The acceleration is constant.
Explanation
When the spring is fully compressed or fully extended when Hook's law forces are the greatest, and this indicates that the acceleration is the greatest. F = ma. Option A is correct because the acceleration is greatest when the spring is fully compressed and when it is fully extended. At the rest length, the acceleration is zero, and at the halfway point between rest and fully extended/compressed positions, the acceleration is less than the maximum value but not constant.
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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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