A weight suspended from an ideal spring oscillates up and down with a period T. If the amplitude of the oscillation is doubled, the period will be:
Correct answer: A. T
- A. T
- B. 1
- C. 2T
- D. T/2
Explanation
The period of a simple harmonic oscillator, such as a weight on an ideal spring, is given by the formula T = 2π√(m/k), where m is the mass and k is the spring constant. The formula shows that the period T is independent of the amplitude of oscillation. Therefore, even if the amplitude is doubled, the period remains the same. Consequently, the correct answer is T. Option B is incorrect as periods are not represented by unitless integers. Option C is incorrect as the period does not double with amplitude. Option D, T/2, is incorrect as the period does not halve.
This question appeared on the ETEA MDCAT 2016 paper, which you can sit online with every answer explained.
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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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