Classical Mechanics (Kibble & Berkshire) · Problem 5.6

Energy conservation — T.W.B. Kibble, F.H. Berkshire

Physics — Mechanics · free-linear-oscillations-critical-damping

Problem

Critical damping Find the general solution of the damped SHM equation (5.9) for the special case of critical damping, that is, when K=ΩK = \Omega. Show that, if the particle is initially released from rest at x=ax = a, then the subsequent motion is given by x=ae−Ωt(1+Ωt).x = ae^{-\Omega t}(1 + \Omega t). Sketch the graph of xx against tt.

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