Suppose a Spring Has Mass $M$ And Spring Constant $k$ And Let $\omega = \sqrt { k / M }$

Suppose a spring has mass $M$ and spring constant $k$ and let $\omega = \sqrt { k / M }$ . Suppose that the damping constant is so small that the damping force is negligible. If an external force $F ( t ) = 8 F _ { 0 } \cos ( \omega t )$ is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to find the equation that describes the motion of the mass.