Show that the total mechanical energy remains constant for a particle executing simple harmonic motion.

Prove that the total mechanical energy remains constant for a ball mass m dropped from a tower of height h.

Find expressions for potential and kinetic energies of a particle executing simple harmonic motion.

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.

If the displacement and the restoring force acting on a particle executing simple harmonic motion are x and F respectively, then F = -kx. Here the negative sign on the right hand side indicates that

If the displacement and the restoring force acting on a particle executing simple harmonic motion are x and F respectively, then F=-kx . Here the negative sign on the right hand side indicates that

Establish the mathematical expression for simple harmonic motion.

The ratio of the masses, time periods and amplitudes of vibration of two particles executing simple harmonic motion are 2 : 1, 2 : 3 and 1 : 2 respectively. Determine the ratio of their mechanical energies.