A simple harmonic oscillator has a total energy E. If the amplitude is halved, w
Practice Questions
Q1
A simple harmonic oscillator has a total energy E. If the amplitude is halved, what will be the new total energy?
E/4
E/2
E
2E
Questions & Step-by-Step Solutions
A simple harmonic oscillator has a total energy E. If the amplitude is halved, what will be the new total energy?
Step 1: Understand that a simple harmonic oscillator has a total energy E that depends on its amplitude.
Step 2: Remember that the total energy E is proportional to the square of the amplitude (E ∝ A²).
Step 3: If the amplitude is halved, we can express the new amplitude as A/2.
Step 4: Calculate the new energy using the new amplitude: E' = k * (A/2)², where k is a constant.
Step 5: Simplify the equation: E' = k * (A²/4) = (k * A²) / 4.
Step 6: Since E = k * A², we can substitute: E' = E / 4.
Step 7: Conclude that if the amplitude is halved, the new total energy will be E/4.
Total Energy in Simple Harmonic Motion – The total energy of a simple harmonic oscillator is given by the formula E = (1/2)kA^2, where k is the spring constant and A is the amplitude. This indicates that energy is proportional to the square of the amplitude.
Effect of Amplitude on Energy – When the amplitude is changed, the total energy changes according to the square of the amplitude. Halving the amplitude results in a reduction of energy to one-fourth of the original.
