Problems 24 through 34 deal with a mass–spring–dashpot system having position function x(t) satisfying Eq. (4). We write x₀ = x(0) and v₀ = x'(0) and recall that

The system is critically damped, overdamped, or underdamped, as specified in each problem.

A body weighing 100 lb (mass m = 3.125 slugs in fps units) is oscillating attached to a spring and a dashpot. Its first two maximum displacements of 6.73 in. and 1.46 in. are observed to occur at times 0.34 s and 1.17 s, respectively. Compute the damping constant (in pound-seconds per foot) and spring constant (in pounds per foot).

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p = c/(2m), w = k/m, and w=w2 - p².