(normalized oscillator dynamics) consider a damped spring–mass system with dynamics mq¨+ cq˙ + kq = f. let ω0 = p k/m be the natural frequency and ζ = c/(2√km) be the damping ratio. a) show that by rescaling the equations, we can write the dynamics in the form q¨+ 2ζω0q˙ + ω2 0q = ω2 0u, (3.39) where u = f/k. this form of the dynamics is that of a linear oscillator with natural frequency ω0 and damping ratio ζ. b) show that the system can be further normalized and written in the form