This sequel of the previous problem will remind you of how you find small oscillations of a classical system near its equilibrium point (they are will teach you how to treat them quantum mechanically to estimate the first few energy eigenvalues of the system, and will train you in making order of magnitude estimates a) assume that the pendulum of the previous problem performs small oscillations around its stable equilibrium point θ-0. approximate the potential energy around this point with a harmonic oscillator potential and find the classical frequency of such small oscillations. b) write the quantum hamiltonian of the pendulum for such small oscillations and find the energy spectrum of these small oscillations. (the energy levels must be expressed in terms of the constants 1, u and ћ.) c) the oscillating molecule is in its first excited state and decays into its ground state by emitting one photon. using the approximation of the previous part, determine the wave- length of the photon.