\documentclass{standalone}

\usepackage{tikz}
\usepackage{pgfplots}
\usepgfplotslibrary{colorbrewer}
\pgfplotsset{compat=1.11}

\pgfplotsset{grid style={dotted, gray!80!white}}

\begin{document}
  \begin{tikzpicture}
    \begin{axis}[height=2in, width=10in, domain=0:10, samples=512, 
      xlabel={Time}, ylabel={Amplitude}, title={$\tau_c = \infty$}, 
      cycle multi list={Set1-4}, xmin=0, xmax=10, 
      xtick={0,1,2,3,4,5,6,7,8,9,10}, xticklabels={$0$, $T$, $2T$, $3T$, $4T$, $5T$, $6T$, $7T$, $8T$, $9T$, $10T$},
      minor x tick num={1},
      grid=major]
      \addplot+[no marks, smooth, ultra thick] {sin(deg(2*pi*x))};
      \addplot+[no marks, smooth, ultra thick] {sin(deg(2*pi*(x + 1/2)))};
    \end{axis}
  \end{tikzpicture}
\end{document}