Suppose you increase the amplitude of oscillation of a mass vibrating on a spring. Which of the following statements about this mass are correct? (There may be more than one correct choice.)A. Its maximum speed increases.B. Its period of oscillation increases.C. Its maximum acceleration increases.D. Its maximum kinetic energy increases.

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To determineThe correct statement about the mass if the amplitude of oscillation of mass is increased.Answer to Problem 2MCPOption (A) its maximum speed increases, option (C) its maximum acceleration increases and (D) its maximum kinetic energy increases.Explanation of SolutionWrite the equation for the maximum speed.      v          m      a      x        =  2  π  f  AHere,       v          m      a      x       is the maximum speed, f is the frequency and A is the amplitude.The maximum speed depends directly on the amplitude of the oscillation. Thus, the maximum speed increases with the increase in the amplitude.Write the equation for the maximum acceleration.      a          m      a      x        =  (  2  π  f      )    2    AHere,       a          m      a      x       is the maximum acceleration.The maximum acceleration depends directly on the amplitude of the oscillation. Thus, the maximum acceleration increases with the increase in the amplitude.Write the equation for the maximum kinetic energy.  K      E          m      a      x        =      1    2    m      v    2    m  a  xHere,   K      E          m      a      x       is the maximum kinetic energy and m is the mass.The maximum kinetic energy depends directly on the square of the maximum speed. The maximum velocity increases with the increase in the amplitude and thus, the maximum kinetic energy increases with the increase in the amplitude.Conclusion:The maximum speed depends directly on the amplitude of the oscillation. Thus, option (A) is correct.The maximum acceleration depends directly on the amplitude of the oscillation. Thus, option (C) is correct.The maximum kinetic energy depends directly on the square on the velocity. As velocity increases with amplitude, maximum kinetic energy also increases. Thus, option (D) is correct.The time period is independent of the amplitude of the oscillation. Thus, option (B) is incorrect.

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