If the amplitude of a simple harmonic oscillator is increased, what happens to i

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Question: If the amplitude of a simple harmonic oscillator is increased, what happens to its total energy? (2021)

Options:

Correct Answer: Increases

Exam Year: 2021

Solution:

The total energy (E) in a simple harmonic oscillator is given by E = (1/2)kA². If amplitude (A) increases, energy increases.

If the amplitude of a simple harmonic oscillator is increased, what happens to its total energy? (2021)

If the amplitude of a simple harmonic oscillator is increased, what happens to its total energy? (2021)

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 (E) of a simple harmonic oscillator is calculated using the formula E = (1/2)kA², where 'k' is a constant related to the system and 'A' is the amplitude.
Step 3: Recognize that amplitude (A) is the maximum distance the oscillator moves from its rest position.
Step 4: If the amplitude (A) increases, you need to look at the formula E = (1/2)kA². Notice that A is squared in the formula.
Step 5: Understand that squaring a larger number (increased amplitude) results in a much larger value. This means that as A increases, A² increases significantly.
Step 6: Since E is directly proportional to A², if A increases, E also increases.
Step 7: Conclude that increasing the amplitude of a simple harmonic oscillator leads to an increase in its total energy.

Total Energy in Simple Harmonic Motion – The total energy of a simple harmonic oscillator is directly proportional to the square of its amplitude.
Amplitude and Energy Relationship – An increase in amplitude leads to an increase in total energy, as energy is proportional to the square of the amplitude.