If a particle of mass m is maintaining an S.H.M. with amplitude A. If the mass is changed to `m/4` then:- what will be the new frequency?

A particle of mass m executes SHM with an amplitude A. If its mass is changed to 1/4 m, then what will be its (i) new frequency and (ii) total energy?

A particle of mass m is executing simple harmonic motion with an amplitude A. If the mass of the particle is reduced by 50%, then what will be its (i) new frequency, (ii) new total energy?

A particle of mass m has momentum p. What is its kinetic energy ?

A particle of mass m executes SHM with amplitude a and frequency n. What is the average kinetic energy of the particle during its motion from the position of equilibrium to the end?

A liquid of mass m_(1) and density rho_(1) is mixed with another liquid of mass m_(2) and density rho_(2) . If the volume of the mixture does not change, then what will be the density of the mixture?