Chapter 2.3, Problem 14P

(a)

To determine

The solution of the differential equation $\frac{du}{dt}=-k\left[u-T\left(t\right)\right]\text{ where }T\left(t\right)=T_0+T_1\cos \omega t$.

(b)

To determine

To draw: The graphs of steady part $S\left(t\right)$ of the solution and the function $T\left(t\right)$ on the same axes. From the graph obtain the amplitude R of the steady  part of $S\left(t\right)$. Also obtain the time lag $\tau$ between the respective maxima of $T\left(t\right)$ and $S\left(t\right)$.

(c)

To determine

The oscillatory part of $S\left(t\right)$ in the form of $R\cos \left[\omega \left(t-\tau \right)\right]$.