If `x,F` and `U` denote the dispalcement, force acting on and potential energy of a particle then

If x, F and U denote the displacement force acting on and potential energy of a particle:

A particle is executing SHM with amplitude A. At displacement x=(-A/4) , force acting on the particle is F, potential energy of the particle is U, velocity of particle is v and kinetic energy is K. Assuming potential energyh to be zero at mean position. At displacement x=A/2

A particle is executing SHM with amplitude A. At displacement x=(-A/4) , force acting on the particle is F, potential energy of the particle is U, velocity of particle is v and kinetic energy is K. Assuming potential energyh to be zero at mean position. At displacement x=A/2

A particle is executing SHM with amplitude A. At displacement x=(-A/4) , force acting on the particle is F, potential energy of the particle is U, velocity of particle is v and kinetic energy is K. Assuming potential energyh to be zero at mean position. At displacement x=A/2

A particle of mass 1 kg is moving X-axis. Its velocity is 6 m//s at x = 0 . Acceleration-displacement curve and potential energy-dispalcement curve of the particle are shown : .

The potential energy U of a body of mass m is given by U = ax + by where x and y are the position coordinates of the particle, the net force acting on the particle is:

A particle of unit mass is moving along the x-axis under the influence of a force and its total energy is conserved. Four possible forms of the potential energy of the particle are given in column-I (a and U0 are constants). Match the potential energies in column-I to the corresponding statement(s) in column-II. {:((A),U_1(x)= (U_0)/(2)[1-(x/a)^(2)]^(2),(P),"the force acting on the particle is zero at x = a."),((B),U_2(x)= (U_0)/(2)(x/a)^(2),(Q),"the force acting on the particle is zero at x = 0."),((C),U_2(x)= (U_0)/(2)(x/a)^(2)exp[-(x/a)],(R),"the force acting on the particle is zero at x = 0."),((D),U_4(x)= (U_0)/(2)[x/a - 1/3 (x/a)^3],(S),"The particle experiences an attractive force towards x = 0 in the region | x | < a"),(,,(T),"The particle with total energy" (U_0)/4 " can oscillate about the point"x = -a.):}