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Question
Two massless springs with spring constants 2k and 9k carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be ______.
Options
1 : 2
3 : 2
3 : 1
2 : 3
MCQ
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Solution
Two massless springs with spring constants 2k and 9k carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be 3 : 2.
Explanation:
In SHM, Vmax = ωA
ωA = constant
`A_1/A_2 = omega_2/omega_1 = sqrt(k_2/m_2 xx m_1/k_1) = sqrt((9k)/100 xx 50/(2k)) = 3/2`
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Velocity and Acceleration in Simple Harmonic Motion
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