Chapter 17.3, Problem 10E

As in Exercise 9, consider a spring with mass m, spring constant k, and damping constant c = 0, and let $\omega =\sqrt{k/m}$. If an external force F(t) = F₀ cos ωt is applied (the applied frequency equals the natural frequency), use the method of undetermined coefficients to show that the motion of the mass is given by

$x(t)=c_1\cos \text{ω}t+c_2\sin \text{ω}t+\frac{F_{{}_0}}{2m\omega }t\sin \text{ω}t$