An oscillator undergoes simple harmonic motion described by the time$-$dependent displacement $z(t)$ that satisfies the differential equation:

$z^{}(t)+Az(t)+B=0$

Determine the position $z_0$ where the object is at equilibrium.

A$)\frac{A}{B}$

B$)-\frac{A}{B}$

$($C$)\frac{B}{A}$

D$)-\frac{B}{A}$

A$-$B

$z(t)=0$

$z^{}(t)=0$

$,\frac{(z^{})(t)}{A}+z(t)+\frac{B}{A}=0$