If the amplitude of a simple harmonic oscillator is tripled, how does the total
Practice Questions
Q1
If the amplitude of a simple harmonic oscillator is tripled, how does the total energy change? (2020)
Increases by 3 times
Increases by 6 times
Increases by 9 times
Remains the same
Questions & Step-by-Step Solutions
If the amplitude of a simple harmonic oscillator is tripled, how does the total energy change? (2020)
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.
Total Energy in Simple Harmonic Motion (SHM) – The total energy of a simple harmonic oscillator is directly proportional to the square of its amplitude.
