(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant 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]

3. 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.

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# Damped Harmonic Oscillator

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