If the amplitude of a simple harmonic oscillator is tripled, how does the total energy change? (2020)

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Q: If the amplitude of a simple harmonic oscillator is tripled, how does the total energy change? (2020)

Solution: Total energy in SHM is proportional to the square of the amplitude. If amplitude is tripled, energy increases by 3^2 = 9 times.

Steps: 8

Step 1: Understand that a simple harmonic oscillator (SHM) is a system that moves back and forth in a regular pattern.
Step 2: Know that the total energy (E) in SHM is related to the amplitude (A) of the motion.
Step 3: Remember the formula for total energy in SHM: E is proportional to A squared (E ∝ A^2).
Step 4: If the amplitude is tripled, it means the new amplitude (A') is 3 times the original amplitude (A).
Step 5: Calculate the new energy using the new amplitude: E' ∝ (3A)^2.
Step 6: Simplify the equation: E' ∝ 9A^2.
Step 7: Since E ∝ A^2, if the original energy is E, then the new energy E' is 9 times the original energy (E' = 9E).
Step 8: Conclude that if the amplitude is tripled, the total energy increases by 9 times.