If the amplitude of a simple harmonic oscillator is halved, how does the total e
Practice Questions
Q1
If the amplitude of a simple harmonic oscillator is halved, how does the total energy change?
Remains the same
Halved
Doubled
Quadrupled
Questions & Step-by-Step Solutions
If the amplitude of a simple harmonic oscillator is halved, how does the total energy change?
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.
Total Energy in Simple Harmonic Motion (SHM) – The total energy of a simple harmonic oscillator is given by the formula E = (1/2)kA^2, where A is the amplitude and k is the spring constant. This indicates that energy is proportional to the square of the amplitude.
