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The variation of kinetic energy with displacement for a spring-mass system executing simple harmonic motion is given by an inverted parabola. The maximum kinetic energy is 16 J, and the kinetic energy becomes zero at displacements of +4 m and -4 m from the mean position. The spring constant of the system is :

Options

  1. A1 N/m
  2. B0.5 N/m
  3. C2 N/m
  4. D4 N/m

Correct answer

C. 2 N/m

Step-by-step solution

The graph of kinetic energy versus displacement is an inverted parabola. The maximum kinetic energy occurs at the mean position (displacement x = 0 ) and represents the total mechanical energy E of the system. Given maximum kinetic energy, E = 16 J. The kinetic energy becomes zero at the extreme positions, which gives the amplitude A of the oscillation. Thus, A = 4 m. The total energy of a spring-mass system is given by: E = 1 2 k A^2 Substituting the given values: 16 = 1 2 k (4)^2 16 = 1 2 k 16 k = 2 N/m. Answer:

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