I need to do frequency domain analysis of the feedback based system shown in the figure (feedback loop block diagram).

For that purpose, I need to use Laplace transformation. Laplace transform of multiplication of two time functions can be calculated easily using standard formulae. But I have a problem in which signal x(t) is multiplied to a time function G cos(\Omega t). So, there is harmonic variation in the gain. I want to make bode plot for the system. Time domain analysis is carried out using Simulink model. But I don't know how frequency domain analysis is possible, as the feedback gain is harmonically varying.

Can some one help me for the problem analytically or numerically? If it can be tackled easily with Simulink or some other software, than please let me know, Thank you.