(a) consider the classical mechanical description of a one-dimensional harmonic os- cillator of mass 0.4kg, with spring constant k damping with b 1.3nsm. 1nm, and subject to linear (i) write down the equation of motion of the oscillator. (ii) assume that the oscillator is initially at r(t 0) (t 0) ims. solve the equation of motion for the oscillator. is the motion over- or under-damped? 0 and has velocity (b) consider the quantum mechanical description of a 1d harmonic oscillator with mass m and angular frequency w. at t 0 the wave-function is given by: (r, t 0) av'o (2) - where o and are the normalized ground and first excited states respectively (i) determine the real positive constant a (ii) give the wave-function as a function of time.