If the amplitude of a simple harmonic oscillator is halved, how does the total energy change?
Practice Questions
1 question
Q1
If the amplitude of a simple harmonic oscillator is halved, how does the total energy change?
Remains the same
Halved
Doubled
Quadrupled
The total energy in SHM is proportional to the square of the amplitude. If amplitude is halved, energy is reduced to (1/2)^2 = 1/4, which is halved.
Questions & Step-by-step Solutions
1 item
Q
Q: If the amplitude of a simple harmonic oscillator is halved, how does the total energy change?
Solution: The total energy in SHM is proportional to the square of the amplitude. If amplitude is halved, energy is reduced to (1/2)^2 = 1/4, which is halved.
Steps: 7
Step 1: Understand that a simple harmonic oscillator (SHM) has energy that depends on its amplitude.
Step 2: Know that the total energy (E) in SHM is proportional to the square of the amplitude (A). This means E ∝ A^2.
Step 3: If the amplitude is halved, we can express this as A' = A/2, where A' is the new amplitude.
Step 4: Calculate the new energy using the new amplitude: E' ∝ (A/2)^2.
Step 5: Simplify the expression: E' ∝ (A^2/4).
Step 6: Since E ∝ A^2, we can say that if the original energy is E, then E' = E/4.
Step 7: Conclude that when the amplitude is halved, the total energy is reduced to one-fourth of the original energy.
