A simple harmonic oscillator has a total energy of 50 J. If the amplitude is dou

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Question: A simple harmonic oscillator has a total energy of 50 J. If the amplitude is doubled, what will be the new total energy?

Options:

Correct Answer: 200 J

Solution:

Total energy in SHM is proportional to the square of the amplitude. If amplitude is doubled, energy increases by a factor of 4.

A simple harmonic oscillator has a total energy of 50 J. If the amplitude is doubled, what will be the new total energy?

A simple harmonic oscillator has a total energy of 50 J. If the amplitude is doubled, what will be the new total energy?

Step 1: Understand that a simple harmonic oscillator has a total energy that depends on its amplitude.
Step 2: Remember 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 square of that change.
Step 3: If the original amplitude is A, and it is doubled, the new amplitude becomes 2A.
Step 4: Calculate the new energy using the relationship: E ∝ A^2. If the original energy is 50 J, the new energy will be proportional to (2A)^2.
Step 5: Calculate (2A)^2 = 4A^2. This means the new energy is 4 times the original energy.
Step 6: Multiply the original energy (50 J) by 4 to find the new total energy: 50 J * 4 = 200 J.

Total Energy in Simple Harmonic Motion (SHM) – The total energy of a simple harmonic oscillator is proportional to the square of its amplitude, expressed as E ∝ A².