Chapter D2.4, Problem 24E

(a)

To determine

To find: The general solution of the differential equation ${y^{\prime }}^{\prime }+2y^{\prime }+\left(w_0{}^2+1\right)y=2\cos t$.

(b)

To determine

To find: The particular solution of the differential equation ${y^{\prime }}^{\prime }+2y^{\prime }+\left(w_0{}^2+1\right)y=2\cos t$ with initial conditions $y\left(0\right)=y^{\prime }\left(0\right)=0$.

(c)

To determine

To identify: The transient and steady state solution from the solution obtain in part (b).

(d)

To determine

To graph: The solution obtained in part (b) for the values of ${\omega }_0=1,2\text{ and 3}$ and note the forcing frequency that produces the steady state oscillations with the greatest amplitude.