The total energy of a particle executing S.H.M. is:
Correct answer: D. Directly proportional to the square of the amplitude
- A. Inversely proportional to the square of the amplitude
- B. Directly proportional to the amplitude
- C. Zero
- D. Directly proportional to the square of the amplitude
Explanation
In simple harmonic motion (S.H.M.), the total energy is a constant sum of kinetic and potential energies, and is given by the formula E = (1/2)mω2A2. Here, E is the total energy, m is the mass, ω is the angular frequency of the oscillation, and A is the amplitude.This equation shows that the total energy is directly proportional to the square of the amplitude, which means that if the amplitude is doubled, the total energy increases by a factor of four.Incorrect options: The energy is not inversely proportional to the square of the amplitude (Option A), nor is it directly proportional to the amplitude (Option B). Option C, stating the energy is zero, is incorrect as the energy in S.H.M. is always a positive value, never zero.
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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