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A particle of mass m moves under the influence of a force F(x) = -kx3, where x is the displacement of the particle from its equilibrium position and k is a positive constant. If the particle is initially at rest at x = a, then what is the velocity of the particle when it passes through its equilibrium position?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A particle of mass m moves under the influence of a force F(x) = -kx3,...
We can use Newton's second law of motion to solve this problem.
The equation of motion for the particle is given by:

We can rewrite this equation as:

We can multiply both sides of this equation byto obtain:

We can integrate both sides of this equation with respect to time to obtain:

At the equilibrium position x = 0, we have:

Therefore, the velocity of the particle when it passes through its equilibrium position is:
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A particle of mass m moves under the influence of a force F(x) = -kx3, where x is the displacement of the particle from its equilibrium position and k is a positive constant. If the particle is initially at rest at x = a, then what is the velocity of the particle when it passes through its equilibrium position?a)b)c)d)Correct answer is option 'B'. Can you explain this answer?
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