Answer
$y=e^{-0.9t}sin(\pi t)$
Work Step by Step
Step 1. Identify the given quantities as $f=0.5Hz, c=0.9, k=1, y(0)=0$ where $y(0)=0$ means that at t=0, the building is in its original position.
Step 2. Use a sine damping model function $y=ke^{-ct}sin(\omega t)$, with $\omega=2\pi f=\pi$, the function becomes $y=e^{-0.9t}sin(\pi t)$
Step 3. Check the initial condition of the function: at t=0, we have y(0)=0
