The dynamics of spreading and recoiling of a liquid droplet after colliding with a partially wet solid surface is studied analytically. Using a mass-spring-damper analogy and based on the variational principle, the energy balance equation is developed, and a nonlinear ordinary differential equation is obtained. Predicted results are validated against the experimental data of others, and it is shown that the model is able to closely predict the effects of inertia, viscosity, and surface tension by reproducing many of the features of droplet dynamics. In addition to the maximum spreading diameter, the conditions under which a droplet recoils or bounces are obtained. Assuming a negligible contact angle hysteresis and no formation of rim or splash, results are discussed for partially wet surfaces in a wide range of viscosity and impact velocities. Compared to other models, which are mostly linear, the proposed model has the advantage of providing a simple and accurate description of droplet dynamics.