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.

(Underdamped) Let x₁ and x₂ be two consecutive local maximum values of x (t). Deduce from the result of Problem 32 that 

The constant Δ = 2πp/ω₁ is called the logarithmic decrement of the oscillation. c = mω₁Δ/π because p = c/(2m).

Transcribed Image Text:

p = c/(2m), w = k/m, and w=w2 - p².