Past exam of the physics A course of the University of Cambridge / 2017 / Paper 2 / Section B / B6 / Response to the added load

Measure downward displacement relative to the former mean equilibrium. The added $M=20\mathrm{kg}$ changes the equilibrium byAssume the load is deposited without a significant impact impulse and then moves with the table. The moving mass becomes $m+M$. Ignoring the tiny pre-existing $10\mathrm{Hz}$ vibration in the sketch, the added-load step response of a supported table isFor the estimated mass, $\beta =0.194{\mathrm{s}}^{-1}$, the envelope time is $1/\beta =5.15\mathrm{s}$, and the period is about $1.13\mathrm{s}$. The table overshoots and rings about the new equilibrium, with the displacement starting continuously at zero and with zero initial slope. A real impact adds an initial-velocity transient; the problem gives no impact history. The residual driven vibration, of order a micrometre, can be superposed.