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Two identical particles perform simple harmonic motion with the same total energy. The first particle has amplitude a1 and the second has amplitude a2. If both particles have equal total mechanical energy, find the ratio a1/a2.

1. 0
2. 1
3. 2
4. 3

Correct answer: 1

Solution

For SHM, total mechanical energy E = (1/2)*m*omega²*A² = (1/2)*k*A². For identical particles, m and omega (or k) are the same. If E1 = E2, then (1/2)*k*a1² = (1/2)*k*a2², which gives a1 = a2, so a1/a2 = 1.

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