Answer
$${\text{2}}$$
Work Step by Step
$$\eqalign{
& {\text{Let }}a\left( t \right) = 2\left( {\frac{{t + \sin t}}{t}} \right) \cr
& \,\,\,\,\,\,\,\,a\left( t \right) = 2\left( {1 + \frac{{\sin t}}{t}} \right) \cr
& {\text{Calculate }}\mathop {\lim }\limits_{t \to \infty } a\left( t \right) \cr
& {\text{ }}\mathop {\lim }\limits_{t \to \infty } a\left( t \right) = \mathop {\lim }\limits_{t \to \infty } 2\left( {1 + \frac{{\sin t}}{t}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2\mathop {\lim }\limits_{t \to \infty } \left( {1 + \frac{{\sin t}}{t}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2\mathop {\lim }\limits_{t \to \infty } \left( 1 \right) + 2\mathop {\lim }\limits_{t \to \infty } \left( {\frac{{\sin t}}{t}} \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2\left( 1 \right) + 2\left( 0 \right) \cr
& \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = 2 \cr
& {\text{Therefore, }} \cr
& {\text{The steady state exits}} \cr
& {\text{The steady - state value is 2}} \cr} $$
