- #1

- 143

- 2

## Homework Statement

$$\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +{ w }^{ 2 }x={ F }_{ 0 }sinwt\quad \quad \quad \quad x(0)=0\quad \quad x'(0)=0$$

## Homework Equations

## The Attempt at a Solution

$$\frac { { d }^{ 2 }x }{ d{ t }^{ 2 } } +{ w }^{ 2 }x={ F }_{ 0 }sinwt\quad \quad \quad \quad x(0)=0\quad \quad x'(0)=0\\ \\ \\ x_{ c }={ c }_{ 1 }coswt+{ c }_{ 2 }sinwt\\ \\ \\ { x }_{ p }=Atsinwt+Btcoswt\\ { x }_{ p }'=wAtcoswt-wBtsinwt\\ { x }_{ p }''=-{ w }^{ 2 }Atsinwt-{ w }^{ 2 }Btcoswt\\ \\ \\ Sub\quad { x }_{ p },\quad { { x }_{ p } }',\quad and\quad { { x }_{ p } }''\quad into\quad the\quad DE\\ \\ \\ 0={ F }_{ 0 }sinwt$$

I'm not sure where to proceed from here.