The potential energy of a particle having mass m is `1/2 momega^2x^2` where `omega` is constant. Prove that its motion is SHM.

Potential energy of a particle is 1/2momega^(2)x^(2) , where m and omega are constants. Prove that the motion of the particle is simple harmonic.

The kinetic energy of a particle is 1/2momega^(2)(A^(2)-x^(2)) , where m, omega and A are constants. Prove that the motion of the particle is simple harmonic.

The speed of a body of mass m, when it is at a distance x from the orign, is v. Its total energy is 1/2mv^(2)+1/2kx^(2) , where k is constant. Prove that the body executes a simple harmonic motion.

The ratio of kinetic energy and potential energy of a particle executing SHM at a distance of 2 cm from its equilibrium position is 3 : 2. What is the amplitude of vibration of the particle?

The potential energy of a particle of mass 0.02 kg moving along x -axis is given by V = Ax(x - 4) J where x is in metres and A is a constant. Which of the following is/are correct statement (s)? (A) The particle is acted upon by a constant force. (B) The particle executes simple harmonic motion. (C) The speed of the particle is maximum at x = 2 m. (D) The period of oscillation of the particle is pi/5 sec.