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PhysicsNEET 2025Spring–mass system and simple pendulum

Oscillations

Two identical point masses P and Q, suspended from two separate massless springs of spring constants k1k_1 and k2k_2 respectively, oscillate vertically. If their maximum speeds are the same, the ratio AQ/APA_Q/A_P of the amplitude AQA_Q of mass Q to the amplitude APA_P of mass P is:

  1. A.k2k1\dfrac{k_2}{k_1}
  2. B.k1k2\dfrac{k_1}{k_2}
  3. C.k2k1\sqrt{\dfrac{k_2}{k_1}}
  4. D.k1k2\sqrt{\dfrac{k_1}{k_2}}✓

Solution

Maximum speed =Aω= A\omega, equal for both: AQωQ=APωPA_Q\omega_Q = A_P\omega_P. With ω∝k\omega \propto \sqrt{k} for equal masses, AQAP=ωPωQ=k1k2\frac{A_Q}{A_P} = \frac{\omega_P}{\omega_Q} = \sqrt{\frac{k_1}{k_2}}.

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