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If the amplitude of a simple harmonic oscillator is doubled, what happens to its

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Question: If the amplitude of a simple harmonic oscillator is doubled, what happens to its total energy?

Options:

  1. It remains the same
  2. It doubles
  3. It quadruples
  4. It halves

Correct Answer: It quadruples

Solution: 

The total energy of a simple harmonic oscillator is proportional to the square of the amplitude. If the amplitude is doubled, the energy increases by a factor of 2^2 = 4.

If the amplitude of a simple harmonic oscillator is doubled, what happens to its

Practice Questions

Q1
If the amplitude of a simple harmonic oscillator is doubled, what happens to its total energy?
  1. It remains the same
  2. It doubles
  3. It quadruples
  4. It halves

Questions & Step-by-Step Solutions

If the amplitude of a simple harmonic oscillator is doubled, what happens to its total energy?
  • Step 1: Understand what a simple harmonic oscillator is. It is a system that moves back and forth in a regular pattern, like a swinging pendulum or a mass on a spring.
  • Step 2: Know that the total energy of a simple harmonic oscillator depends on its amplitude. The amplitude is the maximum distance it moves from its rest position.
  • Step 3: Learn that the total energy (E) is proportional to the square of the amplitude (A). This means if you double the amplitude, the energy changes based on the formula E ∝ A^2.
  • Step 4: If the amplitude is doubled (A becomes 2A), you calculate the new energy: E' = k(2A)^2, where k is a constant.
  • Step 5: Simplify the equation: E' = k(4A^2) = 4(kA^2) = 4E. This shows that the new energy is four times the original energy.
  • Step 6: Conclude that if the amplitude is doubled, the total energy increases by a factor of 4.
  • Total Energy of Simple Harmonic Oscillator – The total energy is proportional to the square of the amplitude, meaning if the amplitude changes, the energy changes by the square of that factor.
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