Differential Equations Quiz
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SECOND-ORDER LINEAR ODES
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A mass-spring system is governed by the differential equation md2xdt2+2γmdxdt+kx=0m\frac{d^2x}{dt^2} + 2\gamma m\frac{dx}{dt} + kx = 0 where m>0m > 0, γ>0\gamma > 0, and k>0k > 0. If the system is critically damped (repeated roots), and the solution with initial conditions x(0)=x0x(0) = x_0 and x′(0)=v0x'(0) = v_0 can be written as x(t)=(A+Bt)e−ωtx(t) = (A + Bt)e^{-\omega t}, which relationship must hold between the parameters?
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