$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

$$\newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} }$$ $$\newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}}$$$$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\id}{\mathrm{id}}$$ $$\newcommand{\Span}{\mathrm{span}}$$ $$\newcommand{\kernel}{\mathrm{null}\,}$$ $$\newcommand{\range}{\mathrm{range}\,}$$ $$\newcommand{\RealPart}{\mathrm{Re}}$$ $$\newcommand{\ImaginaryPart}{\mathrm{Im}}$$ $$\newcommand{\Argument}{\mathrm{Arg}}$$ $$\newcommand{\norm}[1]{\| #1 \|}$$ $$\newcommand{\inner}[2]{\langle #1, #2 \rangle}$$ $$\newcommand{\Span}{\mathrm{span}}$$

1. $$I=e^{-15t}\left(2\cos 5\sqrt{15t}-\frac{6}{\sqrt{31}}\sin 5\sqrt{31}t \right)$$

2. $$I = e^{−20t} (2 \cos 40t − 101 \sin 40t)$$

3. $$I=-\frac{200}{3}e^{-10t}\sin 30t$$

4. $$I = −10e^{−30t} (\cos 40t + 18 \sin 40t)$$

5. $$I = −e^{−40t} (2 \cos 30t − 86 \sin 30t)$$

6. $$I_{p}=-\frac{1}{3}(\cos 10t+2\sin 10t)$$

7. $$I_{p}=\frac{20}{37}(\cos 25t-6\sin 25t)$$

8. $$I_{p} = \frac{3}{13} (8 \cos 50t − \sin 50t)$$

9. $$I_{p} = \frac{20}{123} (17 \sin 100t − 11 \cos 100t)$$

10. $$I_{p} = − \frac{45}{52} (\cos 30t + 8 \sin 30t)$$

12. $$\omega _{0}=1/\sqrt{LC}\quad \text{maximum amplitude }=\sqrt{U^{2}+V^{2}}/R$$