Differential Equations Quiz
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SECOND-ORDER LINEAR ODES
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A critically damped oscillator has the solution x(t)=(A+Bt)e−γtx(t) = (A + Bt)e^{-\gamma t}. If this system is modified to become underdamped with the same natural frequency ω0\omega_0 but damping coefficient reduced by half, and the resulting oscillatory motion has the same initial amplitude AA, what is the ratio of the new oscillation frequency to the original critical damping parameter γ\gamma?
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