Consider a mass–spring system where a 4 kg mass is attached to a massless spring of constant k 196 N/m; the system is set to oscillate on a frictionless, horizontal table. The mass is pulled 25 cm away from the equilibrium position and then released. (a) Use classical mechanics to find the total energy and frequency of oscillations of the system. (b) Treating the oscillator with quantum theory, find the energy spacing between two consecutive energy levels and the total number of quanta involved. Are the quantum effects important in this system?

Consider a mass–spring system where a 4 kg mass is attached to a massless spring of constant k 196 N/m; the system is set to oscillate on a frictionless, horizontal table. The mass is pulled 25 cm away from the equilibrium position and then released. (a) Use classical mechanics to find the total energy and frequency of oscillations of the system. (b) Treating the oscillator with quantum theory, find the energy spacing between two consecutive energy levels and the total number of quanta involved. Are the quantum effects important in this system?