- #1

krnhseya

- 103

- 0

## Homework Statement

Derive...

x(t)=(exp^(-[tex]\zeta[/tex][tex]\omega[/tex]t))*(a1(exp^(i[tex]\omega[/tex]sqrt(1-[tex]\zeta^2[/tex])*t)))+a2(exp^(-i[tex]\omega[/tex]sqrt(1-[tex]\zeta^2[/tex])*t))))

into

x(t)=(exp^(-[tex]\zeta[/tex][tex]\omega[/tex]t))*(A sin ([tex]\omega[/tex]*t + [tex]\varphi[/tex]))

## Homework Equations

n/a

## The Attempt at a Solution

I've managed to get x(t) = (exp^(-[tex]\zeta[/tex][tex]\omega[/tex]t))*((a1(cos[tex]\omega[/tex]*t) + i sin ([tex]\omega[/tex]*t))+(a2(cos[tex]\omega[/tex]*t) - i sin ([tex]\omega[/tex]*t))) then when i simplify things...sin terms cancel out and i end up geting...

exponential term * (a1+a2) * (2cos [tex]\omega[/tex]*t)