Using laplace transform to find the expression for voltage in the circuit
Since you are applying a real excitation, and the circuits is linear and follow the superposition principle you should expect a null imaginary component in the response.
\begin{equation*}
  Im\{u_g(t)\}=0 \rightarrow Im\{u_C(t)\}=0
\end{equation*}
Since you have that:
\begin{equation*}
  Im\{u_C(t)\}=\frac{2}{5}sin(2t)
\end{equation*}
I guess you have a mistake in the Laplace expressions.