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Two massless springs with spring constants 2k and 9k carry masses of 50 g and 100 g respectively at their free ends. Both masses oscillate vertically and their maximum velocities are equal. What is the ratio of their amplitudes (A1: A2)?

1. 1: 2
2. 3: 2
3. 3: 1
4. 2: 3

Correct answer: 3: 2

Solution

For SHM, maximum velocity v_max = A*omega. Setting A1*omega1 = A2*omega2 gives A1/A2 = omega2/omega1 = sqrt(k2/m2) / sqrt(k1/m1). With k1=2k, m1=50g=0.05kg, k2=9k, m2=100g=0.1kg: ratio = sqrt((9k/0.1)/(2k/0.05)) = sqrt(90k/40k) = sqrt(9/4) = 3/2.

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