Amplitude, frequency & primary phase of a particle in S.H. M is 0.04 m. 50 Hz and `pi/3`, respectively. Give mathematical expresstion of its Simple Harmonic Motion.

The time period and amplitude of a particle executing SHM are 10 s and 0.12 m respectively. Find its velocity at a distance 0.04 m from its position of equilibrium.

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.

Amplitude of a particle of mass 0.1 kg executing SHM is 0.1 m. At the mean position its kinetic energy is 8xx10^(-3)J . Find the time period of its vibration.

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 displacement of a particle in S.H.M. varies according to the relation x= 4 (cos pi t +sin pi t ) . The amplitude of the particle is