In a simple harmonic motion, if the amplitude is halved, how does the total energy change?
Correct Answer: Total energy reduces to 1/4.
- Step 1: Understand that in simple harmonic motion, the total energy (E) is related to the amplitude (A).
- Step 2: Know that the formula for total energy in simple harmonic motion is E = k * A^2, where k is a constant.
- Step 3: If the amplitude is halved, it means A becomes A/2.
- Step 4: Substitute the new amplitude into the energy formula: E' = k * (A/2)^2.
- Step 5: Calculate (A/2)^2, which is A^2/4.
- Step 6: So, E' = k * (A^2/4) = (1/4) * (k * A^2) = (1/4) * E.
- Step 7: This means the new total energy is one-fourth of the original energy.
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