New oscillation criteria are established for the second order nonlinear differential equation with a damping term $$ [a(t)\psi(x(t))x'(t)]'+p(t)x'(t)+q(t)f(x(t))=0. $$ These criteria are obtained by using an integral averaging technique. Moreover, we give conditions which ensure that every solution $x(t)$ of the forced second order differential equation with a damping term $$ [a(t)\psi(x(t))x'(t)]'+p(t)x'(t)+q(t)f(x(t))=r(t) $$ satisfies $\liminf_{t\to\infty} |x(t)|=0$.