Derive the equation of motion of a particle of mass m subject to restoring and frictional forces of magnitude kx and b dx/dt respectively, where x is its displacement and k and b are positive constants. Show that x = A exp (– γt) cos (wt + Φ) is only a solution of the equation of motion for 4km > b2 and determine the value of γ, w, γ, A and Φ are real constants. Comment on the physical meaning of this solution. An object oscillates harmonically with a frequency of 0.5 Hz and its amplitude of vibration is halved in 2s. Find a differential equation for the oscillation.