Chapter D2.4, Problem 23E

(a)

To determine

To find: The general solution of the differential equation ${y^{\prime }}^{\prime }+y^{\prime }+\frac{5}{4}y=2\cos \omega t$.

(b)

To determine

To find: The particular solution of the differential equation ${y^{\prime }}^{\prime }+y^{\prime }+\frac{5}{4}y=2\cos \omega t$ 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 $\omega =\frac{1}{2},1\text{ and }\frac{3}{2}$ and note the forcing frequency that produces the steady state oscillations with the greatest amplitude.