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## Homework Statement

The equation for a damped oscillator is d2x/dt2+2βdx/dt +ω02 x = 0. Let ω0=1.0 s−1 and β = 0.54 s−1. The initial values are x(0) = x0 and v(0)=0.

Determine x(t)/x0 at t = 2π/ω0.

## Homework Equations

the solution to equation is given by;

x(t)=e

^{-[itex]\betat[/itex]}(A

_{1}e

^{t[itex]\mu[/itex]}+A

_{2}e

^{-t[itex]\mu[/itex]})

where [itex]\mu[/itex]=[itex]\sqrt{\beta

^{2}-\omega

_{o}

^{2}}[/itex]

## The Attempt at a Solution

A

_{1}=1/2(x

_{o}+(x

_{o}[itex]\beta[/itex])/[itex]\mu[/itex])

A

_{2}=1/2(x

_{o}-(x

_{o}[itex]\beta[/itex])/[itex]\mu[/itex])

The problem I am running into is that the parameter I defined as [itex]\mu[/itex] is imaginary for this case, which keeps throwing me off. My only guess is to ignore the term multiplied by A

_{1}because it is not real, then use only the A

_{2}term and its multiplier because of the -t in its exponent making -i =1. I do not know if this correct and also even the constants A

_{1}and A

_{2}have an i in them as wel.