Differential Equations and Linear Algebra, 4th Edition

Section 5.6

1. 1. $x(t)=2\cos 2t-2\cos 3t$

   

2. 2. $x(t)=\frac{3}{2}\sin 2t-\sin 3t$

   

3. 3. $x(t)=\sqrt{138388}\cos (10t-\alpha )+5\cos (5t-\beta )$ with $\alpha =2\pi -{\tan }^{-1}(1/186)\approx 6.2778$ and $\beta ={\tan }^{-1}(4/3)\approx 0.9273$.

   

4. 4. $x(t)=2\sqrt{106}\cos (5t-\alpha )+10\cos 4t$ with $\alpha =\pi -{\tan }^{-1}(9/5)\approx 2.0779$

   

5. 5. $x(t)=(x_0-C)\cos {\omega }_{0}t+C\cos \omega t$, where $C=F_0/(k-m{\omega }^2)$

6. 7. $x_{\text{sp}}(t)=\frac{10}{13}\cos (3t-\alpha )$ with $\alpha =\pi -{\tan }^{-1}(12/5)\approx 1.9656$

7. 8. $x_{\text{sp}}(t)=\frac{4}{25}\cos (5$