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      Question

      A mass m is suspended from a spring of spring constant

      k and oscillates with amplitude A. The maximum velocity during oscillation is:
      A A Correct Answer Incorrect Answer
      B B Correct Answer Incorrect Answer
      C C Correct Answer Incorrect Answer
      D D Correct Answer Incorrect Answer

      Solution

      Rationale: The motion of a mass-spring system undergoing simple harmonic motion (SHM) is described by the equation x(t) = Acos ( ωt +  φ),   where x(t) is the displacement from the equilibrium position, A is the amplitude, ω is the angular frequency, and ϕ is the phase constant. The velocity of the mass is the first derivative of the displacement with respect to time: The maximum value of the velocity occurs when ∣ sin(ωt + ϕ) ∣ is maximum, which is 1. Therefore, the magnitude of the maximum velocity (vmax​) is: Therefore, the correct answer is option (d).

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