The potential energy of a particle in a space is given by `U=x^(2)+y^(2)` .Find the force associated with this potential energy.

The potential energy U(x) of a particle moving along x - axis is given by U(x)=ax-bx^(2) . Find the equilibrium position of particle.

The potential energy of a particle of mass m is given by U=(1)/(2)kx^(2) for x lt 0 and U = 0 for x ge 0 . If total mechanical energy of the particle is E. Then its speed at x = sqrt((2E)/(k)) is

The potential energy of a particle under a conservative force is given by U ( x) = ( x^(2) -3x) J. The equilibrium position of the particle is at

The potential energy of a particle moving along y axis is given by U(y)= 3y^4+12y^2 ,(where U is in joule and y is in metre). If total mechanical energy is 15 joule, then limits of motion are

The potential energy of a particle of mass 2 kg moving in a plane is given by U = (-6x -8y)J . The position coordinates x and y are measured in meter. If the particle is initially at rest at position (6, 4)m, then

A potential energy function for a two-dimensional force is the form U=3x^2y-7x . Find the force that acts at the point (x,y) .

The potential energy of a particle oscillating along x-axis is given as U=20+(x-2)^(2) Here, U is in joules and x in meters. Total mechanical energy of the particle is 36J . (a) State whether the motion of the particle is simple harmonic or not. (b) Find the mean position. (c) Find the maximum kinetic energy of the particle.

The potential energy function of a particle in the x-y plane is given by U =k(x+y) , where (k) is a constant. The work done by the conservative force in moving a particlae from (1,1) to (2,3) is .

The potential energy function for a particle executing linear SHM is given by V(x)= 1/2kx^2 where k is the force constant of the oscillator. For k = 0.5 Nm^(-1) , the graph of V(x) versus x is shown in the figure A particle of total energy E turns back when it reaches x=pmx_m .if V and K indicate the potential energy and kinetic energy respectively of the particle at x= +x_m ,then which of the following is correct?

The potential energy (in joules ) function of a particle in a region of space is given as: U=(2x^(2)+3y^(2)+2x) Here x,y and z are in metres. Find the maginitude of x compenent of force ( in newton) acting on the particle at point P ( 1m, 2m, 3m).