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Two bodies (M) and (N) of equal masses are suspended from two separate massless springs of spring constants (k_1) and (k_2) respectively. If the two bodies oscillate vertically such that their maximum velocities are equal, the ratio of the amplitude of vibration of (M) to the of (N) is.A. `(k_1)/(k_2)`B. `sqrt(k_1//k_2)`C. `(k_2)/(k_1)`D. `sqrt(k_2//k_1)` |
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Answer» Correct Answer - D Both the bodies oscillate in simple harmonic motion for which the maximum velocities will be `v_(1) = a_(1) omega_(1) = a_(1) xx (2 pi)/(T_(1))` `v_(2) = a_(2) omega_(2) = a_(2) xx (2 pi)/(T_(2))` Given that `v_(1) = v_(2)` `a_(1) xx (2pi)/(T_(1)) = a_(2) xx (2pi)/(T_(2))` `rArr (a_(1))/(a_(2)) = (T_(1))/(T_(2)) = (2 pi sqrt((m)/(k_(1))))/(2pi sqrt((m)/(k_(2)))) = sqrt((k_(2))/(k_(1)))`. |
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