If the amplitude of a simple harmonic oscillator is doubled, how does the total

If the amplitude of a simple harmonic oscillator is doubled, how does the total energy change?

If the amplitude of a simple harmonic oscillator is doubled, how does the total energy change?

Correct Answer: Total energy increases by a factor of 4.

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.

Total Energy in Simple Harmonic Motion – The total energy of a simple harmonic oscillator is given by the formula E = (1/2)kA^2, where E is energy, k is the spring constant, and A is the amplitude. This shows that energy is proportional to the square of the amplitude.