Question
A particle is in equilibrium at O. When it is displaced from O, it experiences a force directly proportional to displacement and directed towards O. Explain the motion of particle.
Solution
Consider a particle of mass m placed at O.
Let it be displaced from O by OB = r.
When the particle is released, it will experience a force F = – kr and starts accelerating towards O.
Let at any instant, the particle be at x from O.
Let the acceleration of the particle be a and velocity be v.
That is, the force acting on the particle is zero but velocity is maximum.
Because of inertia, it will not stop at O, but continue to move in the same direction, i.e. right towards A.
As the particle escapes from O towards right, it experiences the force in the left direction and hence retards.
Ultimately the particle will stop at A.
Restoring force acts at point A and the particle starts accelerating towards left.
When the particle reaches O, force on it will be 0 and velocity will be maximum.
Due to inertia, it will again overshoot O, and due to resorting force it retards and comes to rest at B. Thus, the particle oscillates between B and A.
Let it be displaced from O by OB = r.
When the particle is released, it will experience a force F = – kr and starts accelerating towards O.
Let at any instant, the particle be at x from O.
Let the acceleration of the particle be a and velocity be v.
That is, the force acting on the particle is zero but velocity is maximum.
Because of inertia, it will not stop at O, but continue to move in the same direction, i.e. right towards A.
As the particle escapes from O towards right, it experiences the force in the left direction and hence retards.
Ultimately the particle will stop at A.
Restoring force acts at point A and the particle starts accelerating towards left.
When the particle reaches O, force on it will be 0 and velocity will be maximum.
Due to inertia, it will again overshoot O, and due to resorting force it retards and comes to rest at B. Thus, the particle oscillates between B and A.
