Measuring an AC-voltage at the ouput of a full bridge rectifier
Equation (2) should be: 

$$v(t) = \begin{cases}|(5\sin(100πt)|-2V_D ,&amp; |5\sin(100πt)| &gt; 2V_D \\0 ,&amp; \  |5\sin(100πt)| &lt;= 2V_D\end{cases}$$

The exact reading of a voltage that is not a pure sine wave (zero average voltage) on the AC range of a multimeter depends on whether the multimeter is AC or DC coupled and whether it is true-RMS or average-reading, corrected to RMS. 

Example (resistive load of 1K):