If the amplitude of a simple harmonic oscillator is doubled, how does the total energy change?
Practice Questions
1 question
Q1
If the amplitude of a simple harmonic oscillator is doubled, how does the total energy change?
Remains the same
Doubles
Quadruples
Halves
The total energy in simple harmonic motion is proportional to the square of the amplitude. If amplitude is doubled, energy increases by a factor of 2^2 = 4.
Questions & Step-by-step Solutions
1 item
Q
Q: If the amplitude of a simple harmonic oscillator is doubled, how does the total energy change?
Solution: The total energy in simple harmonic motion is proportional to the square of the amplitude. If amplitude is doubled, energy increases by a factor of 2^2 = 4.
Steps: 7
Step 1: Understand what amplitude means. Amplitude is the maximum distance from the center position in simple harmonic motion.
Step 2: Know that total energy in simple harmonic motion is related to the amplitude. The formula for total energy (E) is E = (1/2) k A^2, where k is a constant and A is the amplitude.
Step 3: If the amplitude (A) is doubled, it means we replace A with 2A in the formula.
Step 4: Substitute 2A into the energy formula: E = (1/2) k (2A)^2.
Step 5: Calculate (2A)^2, which equals 4A^2.
Step 6: Now the energy formula becomes E = (1/2) k (4A^2) = 4 * (1/2) k A^2.
Step 7: This shows that the new energy is 4 times the original energy when the amplitude is doubled.
