If the amplitude of a simple harmonic motion is doubled, what happens to the tot

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Question: If the amplitude of a simple harmonic motion is doubled, what happens to the total energy of the system? (2022)

Options:

Correct Answer: It quadruples

Exam Year: 2022

Solution:

Total energy (E) in SHM is proportional to the square of the amplitude (A). If A is doubled, E becomes 4A^2, hence it quadruples.

If the amplitude of a simple harmonic motion is doubled, what happens to the total energy of the system? (2022)

If the amplitude of a simple harmonic motion is doubled, what happens to the total energy of the system? (2022)

Step 1: Understand that in simple harmonic motion (SHM), the total energy (E) is related to the amplitude (A).
Step 2: Know that the formula for total energy in SHM is E ∝ A^2, which means energy is proportional to the square of the amplitude.
Step 3: If the amplitude (A) is doubled, we can express this as A' = 2A, where A' is the new amplitude.
Step 4: Substitute the new amplitude into the energy formula: E' ∝ (2A)^2.
Step 5: Calculate (2A)^2, which equals 4A^2.
Step 6: This shows that the new total energy (E') is 4 times the original energy (E), meaning it quadruples.

Total Energy in Simple Harmonic Motion – The total energy of a system in simple harmonic motion is proportional to the square of the amplitude, expressed as E ∝ A².