In a simple harmonic motion, if the amplitude is halved, how does the total ener

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Question: In a simple harmonic motion, if the amplitude is halved, how does the total energy change?

Options:

Correct Answer: Halves

Solution:

Total energy E is proportional to the square of the amplitude. If amplitude is halved, energy is reduced to 1/4, hence it halves.

In a simple harmonic motion, if the amplitude is halved, how does the total energy change?

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.

Total Energy in Simple Harmonic Motion – The total energy in simple harmonic motion is proportional to the square of the amplitude, meaning if the amplitude changes, the energy changes according to the square of that change.