As in Exercise 9, consider a spring with mass m, spring con stant k, and damping constant c 0, and let w k m If an external force F(t) F 0 cos wt 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...

As in Exercise 9 xc t C cos wt C sin wt But the natural frequency of the sy ...

As in Exercise 9, consider a spring with mass m, spring con-stant k, and damping constant c

Question:

As in Exercise 9, consider a spring with mass m, spring con-stant k, and damping constant c = 0, and let w = √k/m.
If an external force F(t) = F₀ cos wt 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

Fo x(t) = c1 cos wt + c2 sin wt + 2mw t sin wt