A simple harmonic oscillator has a total energy E. If the amplitude is halved, what will be the new total energy?

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Q: A simple harmonic oscillator has a total energy E. If the amplitude is halved, what will be the new total energy?

Solution: The total energy E is proportional to the square of the amplitude. If the amplitude is halved, the new energy will be E/4.

Steps: 7

Step 1: Understand that a simple harmonic oscillator has a total energy E that depends on its amplitude.
Step 2: Remember that the total energy E is proportional to the square of the amplitude (E ∝ A²).
Step 3: If the amplitude is halved, we can express the new amplitude as A/2.
Step 4: Calculate the new energy using the new amplitude: E' = k * (A/2)², where k is a constant.
Step 5: Simplify the equation: E' = k * (A²/4) = (k * A²) / 4.
Step 6: Since E = k * A², we can substitute: E' = E / 4.
Step 7: Conclude that if the amplitude is halved, the new total energy will be E/4.