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Classical mechanics discusses the behaviour of macroscopic bodies under the influence of forces (without necessarily specifying the origin of these forces). If it's possible, USE MORE SPECIFIC TAGS like [newtonian-mechanics], [lagrangian-formalism], and [hamiltonian-formalism].
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Transient response of a driven damped oscillator to system parameter change
Imagine a damped driven mass spring system with a time-dependent damping coefficient
\begin{equation}
m\frac{d^2x}{dt^2} + b(t)\frac{dx}{dt} + kx = F_0 cos(wt)
\end{equation}
\begin{equation}
b(t) =
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