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A particle constrained to move along the...

A particle constrained to move along the x-axis in a
potential `V=k"x"^(2)` is subjected to an external time dependent
force `vec(f)(t)` here k is a constant, x the distance from the origin,
and t the time. At some time T, when the particle
has zero velocity at x = 0, the external force is removed.
Choose the incorrect options –
(1) Particle executes SHM
(2) Particle moves along +x direction
(3) Particle moves along – x direction
(4) Particle remains at rest

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A particle which is constrained to move along x - axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as F(x)=kx + ax^(3) . Here, k and a are positive constants. For x ge 0 , the functional form of the potential energy U (x) of the particle is