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If the amplitude of a simple harmonic oscillator is doubled, how does the total

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Question: If the amplitude of a simple harmonic oscillator is doubled, how does the total energy change?

Options:

  1. Remains the same
  2. Doubles
  3. Quadruples
  4. Halves

Correct Answer: Quadruples

Solution: 

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

If the amplitude of a simple harmonic oscillator is doubled, how does the total

Practice Questions

Q1
If the amplitude of a simple harmonic oscillator is doubled, how does the total energy change?
  1. Remains the same
  2. Doubles
  3. Quadruples
  4. Halves

Questions & Step-by-Step Solutions

If the amplitude of a simple harmonic oscillator is doubled, how does the total energy change?
Correct Answer: Total energy increases by a factor of 4.
  • Step 1: Understand what amplitude means. Amplitude is the maximum distance from the center position in simple harmonic motion.
  • Step 2: Know that total energy in simple harmonic motion is related to the amplitude. The formula for total energy (E) is E = (1/2) k A^2, where k is a constant and A is the amplitude.
  • Step 3: If the amplitude (A) is doubled, it means we replace A with 2A in the formula.
  • Step 4: Substitute 2A into the energy formula: E = (1/2) k (2A)^2.
  • Step 5: Calculate (2A)^2, which equals 4A^2.
  • Step 6: Now the energy formula becomes E = (1/2) k (4A^2) = 4 * (1/2) k A^2.
  • Step 7: This shows that the new energy is 4 times the original energy when the amplitude is doubled.
  • Total Energy in Simple Harmonic Motion – The total energy of a simple harmonic oscillator is given by the formula E = (1/2)kA^2, where E is energy, k is the spring constant, and A is the amplitude. This shows that energy is proportional to the square of the amplitude.
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