If the amplitude of a simple harmonic oscillator is doubled, what happens to its total energy?
Practice Questions
1 question
Q1
If the amplitude of a simple harmonic oscillator is doubled, what happens to its total energy?
It remains the same
It doubles
It quadruples
It halves
The total energy of a simple harmonic oscillator is proportional to the square of the amplitude. If the amplitude is doubled, the energy increases by a factor of 2^2 = 4.
Questions & Step-by-step Solutions
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Q
Q: If the amplitude of a simple harmonic oscillator is doubled, what happens to its total energy?
Solution: The total energy of a simple harmonic oscillator is proportional to the square of the amplitude. If the amplitude is doubled, the energy increases by a factor of 2^2 = 4.
Steps: 6
Step 1: Understand what a simple harmonic oscillator is. It is a system that moves back and forth in a regular pattern, like a swinging pendulum or a mass on a spring.
Step 2: Know that the total energy of a simple harmonic oscillator depends on its amplitude. The amplitude is the maximum distance it moves from its rest position.
Step 3: Learn that the total energy (E) is proportional to the square of the amplitude (A). This means if you double the amplitude, the energy changes based on the formula E ∝ A^2.
Step 4: If the amplitude is doubled (A becomes 2A), you calculate the new energy: E' = k(2A)^2, where k is a constant.
Step 5: Simplify the equation: E' = k(4A^2) = 4(kA^2) = 4E. This shows that the new energy is four times the original energy.
Step 6: Conclude that if the amplitude is doubled, the total energy increases by a factor of 4.
