A block of mass $m$ is attached to a spring of constant $k$ on a smooth horizontal surface. The block is given an initial velocity $v_0$. If the spring is also attached to a dashpot providing a damping force $F=-cv$, what is the work done by the damping force until the block comes to rest?

1. A.$-0.5m{v}_0^2$
2. B.$-0.5m{v}_0^2-0.5k{x}_{max}^2$
3. C.$0$
4. D.$-0.5k{A}^2$