Consider the forced, undamped oscillator modeled by the equation . The parameter ω0 is the...

Consider the forced, undamped oscillator modeled by the equation . The parameter ω0 is the natural frequency of the unforced system . Write an ODE function M-file for this equation with natural frequency ω0 = 2, and the driving frequency co passed as a parameter.

a) If the driving frequency nearly matches the natural frequency, then a phenomenon called beats occurs. As an example, solve the equation using ode45 with y (0) = 0 and y′(0) = 0 over the interval [0, 60π] with ω = 1.9.

b) If the driving frequency matches the natural frequency, then a phenomenon called resonance occurs. As an example, solve the equation using ode45 with y(0) = 0 and y′(0) = 0 over the interval [0, 60π] with ω = 2.

c) Use the plot3 and comet3 commands, as described in Exercise 17, to create three dimensional plots of the output in parts a) and b).