A system has the transfer-function
$\frac{Y(s)}{X(s)}=\frac{s-\pi}{s+\pi}$
Let $u(t)$ be the unit-step function. The input $x(t)$ that results in a steady-state output $y(t)=\sin \pi t$ is ____________.
- $x(t)=\sin (\pi t) u(t)$
- $x(t)=\sin \left(\pi t+\frac{\pi}{2}\right) u(t)$
- $x(t)=\sin \left(\pi t-\frac{\pi}{2}\right) u(t)$
- $x(t)=\cos \left(\pi t+\frac{\pi}{4}\right) u(t)$