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

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

Options:

Correct Answer: Quadruples

Solution:

The total energy E in SHM is given by E = (1/2)kA². If A is doubled, E becomes (1/2)k(2A)² = 4(1/2)kA², which is quadrupled.

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

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

Step 1: Understand that in simple harmonic motion (SHM), the total energy (E) is calculated using the formula E = (1/2)kA², where k is a constant and A is the amplitude.
Step 2: Identify what happens when the amplitude (A) is doubled. If A becomes 2A, we need to substitute this into the energy formula.
Step 3: Substitute 2A into the energy formula: E = (1/2)k(2A)².
Step 4: Calculate (2A)², which equals 4A².
Step 5: Now substitute this back into the energy formula: E = (1/2)k(4A²).
Step 6: Simplify the equation: E = 4(1/2)kA².
Step 7: Notice that 4(1/2)kA² is 4 times the original energy E = (1/2)kA².
Step 8: Conclude that if the amplitude is doubled, the total energy is quadrupled.

Total Energy in Simple Harmonic Motion – The total energy in simple harmonic motion is directly proportional to the square of the amplitude.
Amplitude and Energy Relationship – Doubling the amplitude results in a fourfold increase in total energy due to the quadratic relationship.