  In the present work, a kind of trigonometric collocation methods based on
Lagrange basis polynomials is developed for effectively solving multi-frequency
oscillatory second-order differential equations
$q^{\prime\prime}(t)+Mq(t)=f\big(q(t)\big)$. The properties of the obtained
methods are investigated. It is shown that the convergent condition of these
methods is independent of $\norm{M}$, which is very crucial for solving
oscillatory systems. A fourth-order scheme of the methods is presented.
Numerical experiments are implemented to show the remarkable efficiency of the
methods proposed in this paper.
