Consider a spring mass dashpot system subjected to a harmonic excitation force of
$$F(t)=F_0 sin(\omega t)$$
The response of a system assuming sufficient time has been passed and the complementary part of the solution has become zero will be
$$x(t)=Xsin(\omega t-\phi)$$
where $$tan\phi=\frac{2\zeta r}{1-r^2}$$ $$r=\frac{\omega}{\omega_n}$$
when $r=1, \phi=90^0$ which means at $t=0, x(0)=-X$
I'm not able to make sense of these results physically. The results say that block at t=0 will be at -X when the excitation force is 0. But I started (t=0) the movement of block at x=0, at which time the force was zero. Results are contradicting my actual conditions. Results say at t=0 x=-X but I started moving the block when x=0