How can i calculate forced response of \$ V_c\$ across the capacitor used transfer funtion?
You have given a transfer function without defining what it is.

Here is the same transfer function with definitions:
$$ \frac{I_L(s)}{V(s)} = \frac{1}{Z_C+Z_L} = \frac{sC}{1+s^2LC} = H_{I_L}$$

Using phasor analysis, \$V(s)\$ is only non-zero when s=0 such that \$V(s=0)=|V|\$. But \$H_{I_L}(s=0) = 0\$

So the forced response of \$I_L\$ is just 0. Interpreting the title question literally, this is the answer.

Here is a relevant transfer function for \$V_C\$:
$$ \frac{V_C(s)}{V(s)} = \frac{Z_C}{Z_C+Z_L} = \frac{1}{1+s^2LC} = H_{V_C}$$

And \$H_{V_C}(s=0) = 1\$

So the forced response is just:
\$V_C(s=0)=|V|\$ which translates to \$v_C(t) = |V|\$ for t>0.

The forced responses given here do not include any natural response.



As you have pointed out, there is an oscillatory transient/natural response that never dies out. One way to obtain the constant for the natural response is to recognize that current through an inductor and voltage across a capacitor are continuous over time. Therefore the initial conditions are \$v_C(t=0)=0\$ and \$i_L(t=0) = 0\$. The first condition can be translated to \$v_L(t=0_+)=|V|\$. Combine with the basic relationship \$v_L = L \frac{di_L}{dt}\$, you can figure out the constant.