The position equation for a oscillator undergoing critical damping is given by
x(t) = Ate^(-γt) + Be^(-γt)
where γ = c/2m
and c is from the original force equation
ma + cv + kx = 0
γ is called the damping factor
my book then goes on to say without explanation that
γ = c/2m = (k/m)^(1/2) = initial angular velocity
I understand the units of c/2m work out to be s^-1 so that's good, but other than that I'm not understanding the relation c/2m = w_initial as well as I want to.
LaTex coming soon to a post near you
x(t) = Ate^(-γt) + Be^(-γt)
where γ = c/2m
and c is from the original force equation
ma + cv + kx = 0
γ is called the damping factor
my book then goes on to say without explanation that
γ = c/2m = (k/m)^(1/2) = initial angular velocity
I understand the units of c/2m work out to be s^-1 so that's good, but other than that I'm not understanding the relation c/2m = w_initial as well as I want to.
LaTex coming soon to a post near you
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