Chapter D2.5, Problem 12E

Solutions to oscillator equations Consider the oscillator equation $y^{″}+b{y}^{\prime }+{\omega }_0^{2}y=F_0\cos \omega t$. For the following parameter values, do the following.

a.    Find the gain and phase lag functions (see Exercises 5–10).

b.    Find the real part of the solution.

c.    Graph the forcing function and the real part of the solution. Verify that the gain function and phase lag function are correct.

12.    b = 3, ω₀ = 1, F₀ = 10, ω = 1