- #1
Warlic
- 32
- 0
Homework Statement
Two things I don't understand; how did he get that omega is sqrt(k/m-(b/2m)^2)
And second; why is it that x(t) = e^(-bt/2m)* cos (omega*t+phi)
shouldnt it rather be; x(t) = c1*cos(ωt) + c2*sin(ωt)
Ah, right. I left out the damping term in the general solution So:Mister T said:Aren't c1 and c2 constants? If so, I see a sinusoid, not a damped sinusoid.
This is exactly the point where I don't know where to go from :P. Where does the c2sin(ωt) part go?gneill said:Ah, right. I left out the damping term in the general solution So:
##x(t) = e^{-\alpha t}(c_1 cos(ωt) + c_2 sin(ωt))##
Go from there. The roots of the auxiliary equation will be complex conjugates of the form ##\alpha ± \omega##, where ##\omega## can be further broken down as ##\omega = \sqrt{\alpha^2 - \omega_o^2}##
See post #3. The sin and cos terms can be amalgamated into a single cos (or sin) term with a constant phase shift.Warlic said:This is exactly the point where I don't know where to go from :P. Where does the c2sin(ωt) part go?
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