A simple harmonic oscillator has a total energy of 50 J. If the amplitude is doubled, what will be the new total energy?
Practice Questions
1 question
Q1
A simple harmonic oscillator has a total energy of 50 J. If the amplitude is doubled, what will be the new total energy?
50 J
100 J
200 J
400 J
Total energy in SHM is proportional to the square of the amplitude. If amplitude is doubled, energy increases by a factor of 4.
Questions & Step-by-step Solutions
1 item
Q
Q: A simple harmonic oscillator has a total energy of 50 J. If the amplitude is doubled, what will be the new total energy?
Solution: Total energy in SHM is proportional to the square of the amplitude. If amplitude is doubled, energy increases by a factor of 4.
Steps: 6
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.
