Assume that the system described by the differential equation mu+γ u+ku = 0 is critically damped and that the initial conditions are u(0) = u0, u(0) = v0. If v0 = 0, show that u → 0 as t → [infinity] but that u is never zero. If u0 is positive, determine a condition on v0 that will ensure that the mass passes through its equilibrium position after it is released.
